extremes of moving averages of random variables with finite endpoint where zj are iid and nonnegative random variables and c 0 are constants satisfying summability conditions at least sufficient to make the random series above converge we suppose that the distribution of zj is regularly varying near 0 and discuss lower tail behavior of finite and infinite linear combinations the behavior is quite different in the two cases for finite linear combinations the lower tail is again regularly varying but for infinite moving averages the lower tail is f varying i e it is in the domain of attraction of a type i extreme value distribution in the sense of minima convergence of point processes based on the moving averages is shown to hold in both the finite and infinite order cases and suitable conclusions are drawn from such convergences a useful analytic tool is asymptotic normality of the esscher transform of the common distribution of the z s the extreme value results of this paper are in terms of minima of the moving average processes but results can be adapted to study maxima of moving averages of random variables in the domain of attraction of the type iii extreme value distribution for maxima

misspecification of noncausal order in autoregressive processes abstract this paper examines noncausal order misspecification in noncausal and mixed processes we consider the constrained maximum likelihood ml estimators of autoregressive parameters obtained when noncausal order s is fixed and potentially different from the true order s 0 the effect of such noncausal order misspecification on the constrained ml estimators of the autoregressive parameters is examined by means of the binding function we find that surprisingly the misspecified estimators are consistent over significant regions of the parameter space next we examine the properties of the unconstrained ml estimator s which is obtained when the objective function is maximized with respect to all model parameters including the noncausal order s in this context we prove the consistency of s and derive its speed of convergence and asymptotic distribution however as the noncausal order is integer valued the problem of identifying s concerns rather model selection than standard estimation we also find that mixed models of different noncausal orders and with the same total autoregressive order are non nested this allows us to propose a new approach for robust identification of the noncausal order from a battery of direct and indirect encompassing tests these tests are based on the difference between the constrained maximum likelihood and indirect inference estimators of the parameters characterizing the mixed causal noncausal dynamics

mathematical analysis of robustness of two level domain decomposition methods with respect to inexact coarse solves convergence of domain decomposition methods rely heavily on the efficiency of the coarse space used in the second level the geneo coarse space has been shown to lead to a fully robust two level schwarz preconditioner which scales well over multiple cores 27 19 as has been proved rigorously in 27 the robustness is due to its good approximation properties for problems with highly heterogeneous material parameters it is available in the finite element packages freefem feel and recently in dune and is implemented as a standalone library in hpddm but the coarse component of the preconditioner can ultimately become a bottleneck if the number of subdomains is very large and exact solves are used it is therefore interesting to consider the effect of approximate coarse solves in this paper robustness of geneo methods is analyzed with respect to approximate coarse solves interestingly the geneo 2 method has to be modified in order to be able to prove its robustness in this context

on the use of inexact subdomain solvers for bddc algorithms the standard bddc balancing domain decomposition by constraints preconditioner is shown to be equivalent to a preconditioner built from a partially subassembled finite element model this results in a system of linear algebraic equations which is much easier to solve in parallel than the fully assembled model the cost is then often dominated by that of the problems on the subdomains an important role is also played both in theory and practice by an averaging operator and in addition exact dirichlet solvers are used on the subdomains in order to eliminate the residual in the interior of the subdomains the use of inexact solvers for these problems and even the replacement of the dirichlet solvers by a trivial extension are considered it is established that one of the resulting algorithms has the same eigenvalues as the standard bddc algorithm and the connection of another with the feti dp algorithm with a lumped preconditioner is also considered multigrid methods are used in the experimental work and under certain assumptions it is established that the iteration count essentially remains the same as when exact solvers are used while considerable gains in the speed of the algorithm can be realized since the cost of the exact solvers grows superlinearly with the size of the subdomain problems while the multigrid methods are linear

weighted sums of i i d random variables attracted to integrals of stable processes under the assumption of the convergence of partial sum processesz n t of i i d random variables to an stable levy processz t 0 2 the convergence of weighted sums f n u dz n u to f u dz u is studied the general convergence result is then applied to examine the domain of attraction of the fractional stable process

robust causality test of infinite variance processes abstract this paper develops a robust causality test for time series with infinite variance innovation processes first we introduce a measure of dependence for vector nonparametric linear processes and derive the asymptotic distribution of the test statistic by taniguchi et al 1996 in the infinite variance case second we construct a weighted version of the generalized empirical likelihood gel test statistic called the self weighted gel statistic in the time domain the limiting distribution of the self weighted gel test statistic is shown to be the usual chi squared one regardless of whether the model has finite variance or not some simulation experiments illustrate satisfactory finite sample performances of the proposed test

uniform convergence of sample second moments of families of time series arrays we consider abstractly defined time series arrays yt t 1 le t le t requiring only that their sample lagged second moments converge and that their end values y1 j t and yt j t be of order less than t for each j ge 0 we show that under quite general assumptions various types of arrays that arise naturally in time series analysis have these properties including regression residuals from a time series regression seasonal adjustments and infinite variance processes rescaled by their sample standard deviation we establish a useful uniform convergence result namely that these properties are preserved in a uniform way when relatively compact sets of absolutely summable filters are applied to the arrays this result serves as the foundation for the proof in a companion paper by findley potscher and wei of the consistency of parameter estimates specified to minimize the sample mean squared multistep ahead forecast error when invertible short memory models are fit to short or long memory time series or time series arrays

bddc and feti dp without matrices or vectors abstract the connection between the bddc balancing domain decomposition by constraints algorithm and the feti dp finite element tearing and interconnecting dual primal algorithm is discussed in the language of function spaces operators and linear functionals

functional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flows we establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying levy measures the limit process is a new class of symmetric stable self similar processes with stationary increments that coincides on a part of its parameter space with a previously described process the normalizing sequence and the limiting process are determined by the ergodic theoretical properties of the flow underlying the integral representation of the process these properties can be interpreted as determining how long the memory of the stationary infinitely divisible process is we also establish functional convergence in a strong distributional sense for conservative pointwise dual ergodic maps preserving an infinite measure

mean payoff games with partial observation mean payoff games are important quantitative models for open reactive systems they have been widely studied as games of perfect information in this paper we investigate the algorithmic properties of several subclasses of mean payoff games where the players have asymmetric information about the state of the game these games are in general undecidable and not determined according to the classical definition we show that such games are determined under a more general notion of winning strategy we also consider mean payoff games where the winner can be determined by the winner of a finite cycle forming game this yields several decidable classes of mean payoff games of asymmetric information that require only finite memory strategies including a generalization of perfect information games where positional strategies are sufficient we give an exponential time algorithm for determining the winner of the latter

parameterized pursuit evasion games we study the parameterized complexity of four variants of pursuit evasion on graphs seeded pursuit evasion short seeded pursuit evasion directed pursuit evasion and short directed pursuit evasion both seeded pursuit evasion and short seeded pursuit evasion are played on undirected graphs with given starting positions for both the cops and the robber directed pursuit evasion and its short variant are played on directed graphs with the players free to choose their starting positions we show for seeded pursuit evasion and directed pursuit evasion that finding a winning strategy for the cops is aw hard when we parameterize by the number of cops further we show that the short k move variants of these problems short seeded pursuit evasion and short directed pursuit evasion are aw complete when we parameterize by both the number of cops and turns

the complexity of stochastic games abstract we consider the complexity of stochastic games simple games of chance played by two players we show that the problem of deciding which player has the greatest chance of winning the game is in the class np co np

a functional limit theorem for dependent sequences with infinite variance stable limits under an appropriate regular variation condition the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non gaussian stable random variable a functional version of this is known to be true as well the limit process being a stable levy process the main result in the paper is that for a stationary regularly varying sequence for which clusters of high threshold excesses can be broken down into asymptotically independent blocks the properly centered partial sum process still converges to a stable levy process due to clustering the levy triple of the limit process can be different from the one in the independent case the convergence takes place in the space of cadlag functions endowed with skorohod s m 1 topology the more usual j 1 topology being inappropriate as the partial sum processes may exhibit rapid successions of jumps within temporal clusters of large values collapsing in the limit to a single jump the result rests on a new limit theorem for point processes which is of independent interest the theory is applied to moving average processes squared garch 1 1 processes and stochastic volatility models

a three level bddc algorithm for a saddle point problem bddc algorithms have previously been extended to the saddle point problems arising from mixed formulations of elliptic and incompressible stokes problems in these two level bddc algorithms all iterates are required to be in a benign space a subspace in which the preconditioned operators are positive definite this requirement can lead to large coarse problems which have to be generated and factored by a direct solver at the beginning of the computation and they can ultimately become a bottleneck an additional level is introduced in this paper to solve the coarse problem approximately and to remove this difficulty this three level bddc algorithm keeps all iterates in the benign space and the conjugate gradient methods can therefore be used to accelerate the convergence this work is an extension of the three level bddc methods for standard finite element discretization of elliptic problems and the same rate of convergence is obtained for the mixed formulation of the same problems estimate of the condition number for this three level bddc methods is provided and numerical experiments are discussed

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

model identification for infinite variance autoregressive processes abstract we consider model identification for infinite variance autoregressive time series processes it is shown that a consistent estimate of autoregressive model order can be obtained by minimizing akaike s information criterion and we use all pass models to identify noncausal autoregressive processes and estimate the order of noncausality the number of roots of the autoregressive polynomial inside the unit circle in the complex plane we examine the performance of the order selection procedures for finite samples via simulation and use the techniques to fit a noncausal autoregressive model to stock market trading volume data

a domain decomposition method with lagrange multipliers and inexact solvers for linear elasticity a new domain decomposition method with lagrange multipliers for elliptic problems is introduced it is based on a reformulation of the well known finite element tearing and interconnecting feti method as a saddle point problem with both primal and dual variables as unknowns the resulting linear system is solved with block structured preconditioners combined with a suitable krylov subspace method this approach allows the use of inexact subdomain solvers for the positive definite subproblems it is shown that the condition number of the preconditioned saddle point problem is bounded independently of the number of subregions and depends only polylogarithmically on the number of degrees of freedom of individual local subproblems numerical results are presented for a plane stress cantilever membrane problem

the durbin watson ratio under infinite variance errors abstract this paper studies the properties of the von neumann ratio for time series with infinite variance our asymptotics cover the null of iid variates and general moving average ma alternatives regression residuals are also considered in the static regression model the durbin watson statistic has the same limit distribution as the von neumann ratio in dynamic models the results are more complex in finite variance models our results specialize to those of the durbin h statistic and equivalent lm test asymptotics some monte carlo results are reported illustrating the effects of infinite variance errors and regressors in finite samples

the neumann dirichlet domain decomposition method with inexact solvers on the subdomains we consider the neumann dirichlet domain decomposition method for the solution of linear elliptic boundary value problems we study the following question suppose that the auxiliary problems on the subdomains are not solved exactly but only with a fixed mesh size independent accuracy does the speed of convergence remain mesh size independently bounded we show that the answer is no in general but that mesh size independent convergence can be obtained if the accuracy requirement on the subsolvers becomes increasingly severe as the mesh size tends to zero

a unified dual primal finite element tearing and interconnecting approach for incompressible stokes equations summary a unified framework of dual primal finite element tearing and interconnecting feti dp algorithms is proposed for solving the system of linear equations arising from the mixed finite element approximation of incompressible stokes equations a distinctive feature of this framework is that it allows using both continuous and discontinuous pressures in the algorithm whereas previous feti dp methods only apply to discontinuous pressures a preconditioned conjugate gradient method is used in the algorithm with either a lumped or a dirichlet preconditioner and scalable convergence rates are proved this framework is also used to describe several previously developed feti dp algorithms and greatly simplifies their analysis numerical experiments of solving a two dimensional incompressible stokes problem demonstrate the performances of the discussed feti dp algorithms represented under the same framework copyright 2012 john wiley sons ltd

deciding the winner in k rounds for disjoint arrows a new combinatorial partizan game we consider disjoint arrows a new bounded length two player partizan combinatorial game in this game the two players alice and bob alternate in choosing vertices on a directed graph and no player is allowed to select a vertex previously selected at each round alice selects a vertex u and bob has to reply choosing a new vertex in the out neighborhood of u the first player who cannot move loses we prove that deciding whether bob can endure k rounds when k is part of the input is a pspace complete problem moreover we prove that the parameterized version of the problem is aw complete thus we provide a new member for the small set of problems known complete for the class aw

large deviations estimates in burgers turbulence with stable noise initial data we consider the inviscid burgers equation where the initial datum is given by a stable levy noise the asymptotic behavior of the tail distribution of the solution is described the decay is much faster in the case when the stable noise is completely skewed to the left

an optimal on line algorithm for metrical task system in practice almost all dynamic systems require decisions to be made on line without full knowledge of their future impact on the system a general model for the processing of sequences of tasks is introduced and a general on line decision algorithm is developed it is shown that for an important class of special cases this algorithm is optimal among all on line algorithms specifically a task system s d for processing sequences of tasks consists of a set s of states and a cost matrix d where d i j is the cost of changing from state i to state j we assume that d satisfies the triangle inequality and all diagonal entries are 0 the cost of processing a given task depends on the state of the system a schedule for a sequence t 1 t 2 t k of tasks is a sequence s 1 s 2 s k of states where s i is the state in which t i is processed the cost of a schedule is the sum of all task processing costs and the state transition costs incurred an on line scheduling algorithm is one that chooses s i only knowing t 1 t 2 t i such an algorithm is w competitive if on any input task sequence its cost is within an additive constant of w times the optimal offline schedule cost the competitive ratio w s d is the infimum w for which there is a w competitive on line scheduling algorithm for s d it is shown that w s d 2 s 1 for every task system in which d is symmetric and w s d o s 2 for every task system finally randomized on line scheduling algorithms are introduced it is shown that for the uniform task system in which d i j 1 for all i j the expected competitive ratio w s d o log s

an invariance principle for sums and record times of regularly varying stationary sequences we prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time after deducing the limiting distribution for individual clusters of extremes we present a new type of point process convergence theorem it is designed to preserve the entire information about the temporal ordering of observations which is typically lost in the limit after time scaling by going beyond the existing asymptotic theory we are able to prove a new functional limit theorem its assumptions are satisfied by a wide class of applied time series models for which standard limiting theory in the space d of cadlag functions does not apply to describe the limit of partial sums in this more general setting we use the space e of so called decorated cadlag functions we also study the running maximum of partial sums for which a corresponding functional theorem can be still expressed in the familiar setting of space d we further apply our method to analyze record times in a sequence of dependent stationary observations even when their marginal distribution is not necessarily regularly varying under certain restrictions on dependence among the observations we show that the record times after scaling converge to a relatively simple compound scale invariant poisson process

games on interval and permutation graph representations we describe combinatorial games on graphs in which two players antagonistically build a representation of a subgraph of a given graph we show that for a large class of these games determining whether a given instance is a winning position for the next player is pspace hard in contrast we give polynomial time algorithms for solving some versions of the games on trees

lower bounds for nonoverlapping domain decomposition preconditioners in two dimensions lower bounds for the condition numbers of the preconditioned systems are obtained for the bramble pasciak schatz substructuring preconditioner and the neumann neumann preconditioner in two dimensions they show that the known upper bounds are sharp

the complexity of mean payoff games on graphs abstract we study the complexity of finding the values and optimal strategies of mean payoff games on graphs a family of perfect information games introduced by ehrenfeucht and mycielski and considered by gurvich karzanov and khachiyan we describe a pseudo polynomial time algorithm for the solution of such games the decision problem for which is in np conp finally we describe a polynomial reduction from mean payoff games to the simple stochastic games studied by condon these games are also known to be in np conp but no polynomial or pseudo polynomial time algorithm is known for them

inexact feti dp methods inexact feti dp domain decomposition methods are considered preconditioners based on formulations of feti dp as a saddle point problem are used which allow for an inexact solution of the coarse problem a positive definite reformulation of the preconditioned saddle point problem which also allows for approximate solvers is considered as well in the formulation that iterates on the original feti dp saddle point system it is also possible to solve the local neumann subdomain problems inexactly given good approximate solvers for the local and coarse problems convergence bounds of the same quality as for the standard feti dp methods are obtained numerical experiments which compare the convergence of the inexact methods with that of standard feti dp are shown for 2d and 3d elasticity using gmres and cg as krylov space methods based on parallel computations a comparison of one variant of the inexact feti dp algorithms and the standard feti dp method is carried out and similar parallel performance is achieved parallel scalability of the inexact variant is also demonstrated it is shown that for a very large number of subdomains and a very large coarse problem the inexact method can be superior copyright 2006 john wiley sons ltd

a preconditioner for substructuring based on constrained energy minimization a preconditioner for substructuring based on constrained energy minimization concepts is presented the preconditioner is applicable to both structured and unstructured meshes and offers a straightforward approach for the iterative solution of second and fourth order structural mechanics problems the approach involves constraints associated with disjoint sets of nodes on substructure boundaries these constraints provide the means for preconditioning at both the substructure and global levels numerical examples are presented that demonstrate the good performance of the method in terms of iterations compute time and condition numbers of the preconditioned equations

on the properties of the coefficient of determination in regression models with infinite variance variables abstract we examine the asymptotic properties of the coefficient of determination r 2 in models with stable random variables if the regressor and error term share the same index of stability 2 we show that the r 2 statistic does not converge to a constant but has a nondegenerate distribution on the entire 0 1 interval we provide closed form expressions for the cumulative distribution function and probability density function of this limit random variable and we show that the density function is unbounded at 0 and 1 if the indices of stability of the regressor and error term are unequal we show that the coefficient of determination converges in probability to either 0 or 1 depending on which variable has the smaller index of stability irrespective of the value of the slope coefficient in an empirical application we revisit the fama and macbeth 1973 two stage regression and demonstrate that in the infinite variance case the r 2 statistic of the second stage regression converges to 0 in probability even if the slope coefficient is nonzero we deduce that a small value of the r 2 statistic should not in itself be used to reject the usefulness of a regression model

a parallel implementation of an iterative substructuring algorithm for problems in three dimensions numerical results from a parallel implementation of a class of iterative substructuring algorithms are reported the algorithms are for solving self adjoint elliptic partial differential equations in three dimensions results are given for several variants of the algorithm in the first variant exact interior solvers are used in the second one multigrid v cycle is used to solve the interior problems approximately the results are compared with theoretical behavior of the algorithm reported in previous work a numerical experiment involving the equations of linear elasticity is also included

balancing neumann neumann methods for incompressible stokes equations this paper describes the unerlying mathematical model and the balancing neumann neumann methods are introduced and studied for incompressible stokes equations discretized with mixed finite or spectral elements with discontinuous pressures after decomposing the original domain of the problem into nonoverlapping subdomains the interior unknowns which are the interior velocity component and all except the constant pressure component of each subdomain problem are implicitly eliminated the resulting saddle point schur complement is solved with a krylov space method with a balancing neumann neumann preconditioner based on the solution of a coarse stokes problem with a few degrees of freedom per subdomain and on the solution of local stokes problems with natural neumann velocity and essential boundary conditions on the subdomains this preconditioner is of hybrid form in which the coarse problem is treated multiplicatively while the local problems are treated additively the condition number of the preconditioned operator is independent of the number of subdomains and is bounded from above by the product of the square of the logarithm of the local number of unknowns in each subdomain and the inverse of the inf sup constants of the discrete problem and of the coarse subproblem numerical results show that the method is quite fast they are also fully consistent with the theory

on the complexity of the misere version of three games played on graphs we investigate the complexity of finding a winning strategy for the misere version of three games played on graphs two variants of the game nimg introduced by stockmann in 2004 and the game vertex geography on both directed and undirected graphs we show that on general graphs those three games are pspace hard or complete for one pspace hard variant of nimg we find an algorithm to compute an effective winning strategy in time o v g e g when g is a bipartite graph

three level bddc in two dimensions balancing domain decomposition by constraints bddc methods are non overlapping iterative substructuring domain decomposition methods for the solution of large sparse linear algebraic systems arising from discretization of elliptic boundary value problems they are similar to the balancing neumann neumann algorithm however in bddc methods a small number of continuity constraints are enforced across the interface and these constraints form a new coarse global component an important advantage of using such constraints is that the schur complements that arise in the computation will all be strictly positive definite the matrix of the coarse problem is generated and factored by direct solvers at the beginning of the computation however this problem can ultimately become a bottleneck if the number of subdomains is very large in this paper two three level bddc methods are introduced for solving the coarse problem approximately in two dimensional space while still maintaining a good convergence rate estimates of the condition numbers are provided for the two three level bddc methods and numerical experiments are also discussed copyright 2006 john wiley sons ltd

hydraulic conductivity velocity and the order of the fractional dispersion derivative in a highly heterogeneous system 1 a one dimensional fractional order advection dispersion equation accurately models the movement of the core of the tritium plume at the highly heterogeneous made site an a priori estimate of the parameters in that equation including the order of the fractional dispersion derivative was based on the assumption that the observed power law heavy tail of the hydraulic conductivity k field would create a similarly distributed velocity field monte carlo simulations were performed to test this hypothesis results from the monte carlo analysis show that heavy tailed k fields do give rise to heavy tailed velocity fields however the exponent of the power law the tail parameter describing these two distributions is not necessarily the same the tail parameter that characterizes a velocity distribution is not solely dependent on the tail parameter that characterizes the k distribution the k field must also have long range dependence so that water may flow through relatively continuous high k channels

external theory for stochastic processes abstract the purpose of this paper is to provide an overview of the asymptotic distributional theory of extreme values for a wide class of dependent stochastic sequences and continuous parameter processes the theory contains the standard classical extreme value results for maxima and extreme order statistics as special cases but is richer on account of the diverse behavior possible under dependence in both discrete and continuous time contexts emphasis is placed on stationary cases but other important classes e g mark of sequences are included significant ideas and methods are described rather than details and in particular the nature and role of important underlying point processes such as exceedances and upcrossings are emphasized applications are given to particular classes of process e g normal moving average and connections with related theory such as convergence of sums are indicated

an iterative substructuring method for maxwell s equations in two dimensions iterative substructuring methods also known as schur complement methods form an important family of domain decomposition algorithms they are preconditioned conjugate gradient methods where solvers on local subregions and a solver on a coarse mesh are used to construct the preconditioner for conforming finite element approximations of h 1 it is known that the number of conjugate gradient steps required to reduce the residual norm by a fixed factor is independent of the number of substructures and that it grows only as the logarithm of the dimension of the local problem associated with an individual substructure in this paper the same result is established for similar iterative methods for low order n e d e lec finite elements which approximate hcurl in two dimensions results of numerical experiments are also provided

self weighted least absolute deviation estimation for infinite variance autoregressive models summary how to undertake statistical inference for infinite variance autoregressive models has been a long standing open problem to solve this problem we propose a self weighted least absolute deviation estimator and show that this estimator is asymptotically normal if the density of errors and its derivative are uniformly bounded furthermore a wald test statistic is developed for the linear restriction on the parameters and it is shown to have non trivial local power simulation experiments are carried out to assess the performance of the theory and method in finite samples and a real data example is given the results are entirely different from other published results and should provide new insights for future research on heavy tailed time series

n by n checkers is exptime complete the game of checkers can easily be generalized to be played on an n by n board and the complexity of deciding questions about positions regarded as a function of n this paper considers mainly the question of whether a particular player can force a win from a given position and also the question of what is the best move in a given position each of these problems is shown to be complete in exponential time this means that any algorithm to solve them must take time which rises exponentially with respect to some power of n and moreover that they are amongst the hardest problems with such a time bound for instance if there are any problems solvable in exponential time but not in polynomial space then these two problems are amongst them

on the extremes of a class of non linear processes with heavy tailed innovations the aim of this paper is to look at the limiting form of certain empirical point processes induced by a particular class of non linear processes generated by heavy tailed innovations such asymptotic results will be highly useful in obtaining the weak limiting behavior of various functionals of the underlying process including the asymptotic distribution of upper and lower order statistics in particular we investigate the maximum limiting distribution and its corresponding extremal index the results are applied to the study of the extremal properties of bilinear processes

an iterative substructuring method for raviart thomas vector fields in three dimensions the iterative substructuring methods also known as schur complement methods form one of two important families of domain decomposition algorithms they are based on a partitioning of a given region on which the partial differential equation is defined into nonoverlapping substructures the preconditioners of these conjugate gradient methods are then given in terms of local problems defined on individual substructures and pairs of substructures and in addition a global problem of low dimension an iterative method of this kind is introduced for the lowest order raviart thomas finite elements in three dimensions and it is shown that the condition number of the relevant operator is independent of the number of substructures and grows only as the square of the logarithm of the number of unknowns associated with an individual substructure the theoretical bounds are confirmed by a series of numerical experiments

cyclical games with prohibitions we consider a certain combinatorial game on a digraph for two cases of the price function for one case the game in question extends the cyclical game studied in ehrenfeucht and mycielski 1979 and gurvitch karzanov and khachiyan 1988 which in its turn is a generalization of the well known problem of finding a minimum mean cycle in an edge weighted digraph we prove the existence of optimal uniform stationary strategies for both cases and give algorithms to find such strategies

a subexponential randomized algorithm for the simple stochastic game problem we describe a randomized algorithm for the simple stochastic game problem that requires 2o n expected operations for games with n vertices this is the first subexponential time algorithm for this problem

dual primal feti methods for linear elasticity dual primal feti methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations as in primal iterative substructuring methods while most of the constraints are enforced by lagrange multipliers as in one level feti methods these methods are used to solve the large algebraic systems of equations that arise in elliptic finite element problems the purpose of this article is to develop strategies for selecting these constraints which are enforced throughout the iterations such that good convergence bounds are obtained that are independent of even large changes in the stiffness of the subdomains across the interface between them the algorithms are described in terms of a change of basis that has proven to be quite robust in practice a theoretical analysis is provided for the case of linear elasticity and condition number bounds are established that are uniform with respect to arbitrarily large jumps in the young s modulus of the material and otherwise depend only polylogarithmically on the number of unknowns of a single subdomain the strategies have already proven quite successful in large scale implementations of these iterative methods 2006 wiley periodicals inc

on some estimates based on sample behavior near high level excursions let j be a stationary sequence of weakly dependent random variables and letm n k be thek th largest value of j 1 j n the estimation of the parameters of the asymptotic distribution ofm n k is considered using a procedure motivated by a limit theorem pertaining to the point process sum nolimits j delta j n n bar f xi j a number of statistical issues concerning the procedure including how to select the tuning parameters are addressed the second problem that we consider is the estimation of the filter of a moving average process with heavy tails in particular the investigation covers the moving average stable process motivated by ideas in rootzen 1978 our estimator uses information contained in the sample behavior of the process near the largest excursion

maximum likelihood estimation for α stable autoregressive processes we consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non gaussian stable noise a nondegenerate limiting distribution is given for maximum likelihood estimators of the parameters of the autoregressive model equation and the parameters of the stable noise distribution the estimators for the autoregressive parameters are n 1 consistent and converge in distribution to the maximizer of a random function the form of this limiting distribution is intractable but the shape of the distribution for these estimators can be examined using the bootstrap procedure the bootstrap is asymptotically valid under general conditions the estimators for the parameters of the stable noise distribution have the traditional n 1 2 rate of convergence and are asymptotically normal the behavior of the estimators for finite samples is studied via simulation and we use maximum likelihood estimation to fit a noncausal autoregressive model to the natural logarithms of volumes of wal mart stock traded daily on the new york stock exchange

stable limits for sums of dependent infinite variance random variables the aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution conditions for this convergence to hold are known in the literature however most of these results are qualitative in the sense that the parameters of the limit distribution are expressed in terms of some limiting point process in this paper we will be able to determine the parameters of the limiting stable distribution in terms of some tail characteristics of the underlying stationary sequence we will apply our results to some standard time series models including the garch 1 1 process and its squares the stochastic volatility models and solutions to stochastic recurrence equations

inference in arch and garch models with heavy tailed errors arch and garch models directly address the dependency of conditional second moments and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present these include financial time series which can be particularly heavy tailed however little is known about properties of arch or garch models in the heavy tailed setting and no methods are available for approximating the distributions of parameter estimators there in this paper we show that for heavy tailed errors the asymptotic distributions of quasi maximum likelihood parameter estimators in arch and garch models are nonnormal and are particularly difficult to estimate directly using standard parametric methods standard bootstrap methods also fail to produce consistent estimators to overcome these problems we develop percentile t subsample bootstrap approximations to estimator distributions studentizing is employed to approximate scale and the subsample bootstrap is used to estimate shape the good performance of this approach is demonstrated both theoretically and numerically

monadic second order evaluations on tree decomposable graphs abstract every graph generated by a hyperedge replacement graph grammar can be represented by a tree namely the derivation tree of the derivation sequence that produced it certain functions on graphs can be computed recursively on the derivation trees of these graphs by using monadic second order logic and semiring homomorphisms we describe in a single formalism a large class of such functions polynomial and even linear algorithms can be constructed for some of these functions we unify similar results obtained by takamizawa 1982 bern 1987 arnborg 1991 and habel 1989

stationary bubble equilibria in rational expectation models abstract a linear rational expectation model with current expectations admits a unique linear stationary dynamic equilibrium only under specific restrictions on the parameter values this paper shows that in general there is a multiplicity of stationary dynamic equilibria due to the existence of nonlinear stationary equilibria these nonlinear stationary equilibria are consistent with the self fulfilling prophecies that characterize the rational expectation equilibria and can display speculative bubbles volatility induced mean reversion and or stochastic autoregressive patterns they are also compatible with the transversality conditions when the model involves intertemporal optimization the stationary nonlinear dynamic equilibria are economically relevant their analysis requires revised methods of identification for the stationary equilibrium impulse response analysis and estimation techniques which are presented in this paper standard econometric and economic methods which ignore the nonlinear stationary solutions provide misleading outcomes which may affect the validity of an economic policy or portfolio strategy

a large deviations approach to limit theory for heavy tailed time series in this paper we propagate a large deviations approach for proving limit theory for generally multivariate time series with heavy tails we make this notion precise by introducing regularly varying time series we provide general large deviation results for functionals acting on a sample path and vanishing in some neighborhood of the origin we study a variety of such functionals including large deviations of random walks their suprema the ruin functional and further derive weak limit theory for maxima point processes cluster functionals and the tail empirical process one of the main results of this paper concerns bounds for the ruin probability in various heavy tailed models including garch stochastic volatility models and solutions to stochastic recurrence equations

vertex nim played on graphs given a graph g with positive integer weights on the vertices and a token placed on some current vertex u two players alternately remove a positive integer weight from u and then move the token to a new current vertex adjacent to u when the weight of a vertex is set to 0 it is removed and its neighborhood becomes a clique the player making the last move wins this adaptation of nim on graphs is called vertexnim and slightly differs from the game vertex nimg introduced by stockman in 2004 vertexnim can be played on both directed or undirected graphs in this paper we study the complexity of deciding whether a given game position of vertexnim is winning for the first or second player in particular we show that for undirected graphs this problem can be solved in quadratic time our algorithm is also available for the game vertex nimg thus improving email protected s exptime algorithm in the directed case we are able to compute the winning strategy in polynomial time for several instances including circuits or digraphs with self loops

extremes of volterra series expansions with heavy tailed innovations abstract in this paper we look at the extremal behavior of volterra series expansions generated by heavy tailed innovations via a point process formulation volterra series expansions are known to be the most general nonlinear representation for any stationary sequence the so called complete convergence theorem on point processes we prove enable us to give in detail the weak limiting behavior of various functionals of the underlying process including the asymptotic distribution of upper and lower order statistics in particular we investigate the limiting distribution of the sample maxima and the corresponding extremal index the study of the extremal properties of finite order volterra series expansions would be highly valuable in understanding the extremal behavior of nonlinear processes as well as understanding of order identification and adequacy of volterra series when used as models in signal processing in fact such extremal properties may suggest a way of finding the order of a finite volterra expansions which is consistent with the nonlinearities of the observed process

periodic moving averages of random variables with regularly varying tails in this paper we establish the basic asymptotic theory for periodic moving averages of i i d random variables with regularly varying tails the moving average coefficients are allowed to vary according to the season a simple reformulation yields the corresponding results for moving averages of random vectors our main result is that when the underlying random variables have finite variance but infinite fourth moment the sample autocorrelations are asymptotically stable it is well known in this case that sample autocorrelations in the classical stationary moving average model are asymptotically normal

local explosion modelling by non causal process the noncausal autoregressive process with heavy tailed errors possesses a nonlinear causal dynamics which allows for unit root local explosion or asymmetric cycles often observed in economic and financial time series it provides a new model for multiple local explosions in a strictly stationary framework the causal predictive distribution displays surprising features such as the existence of higher moments than for the marginal distribution or the presence of a unit root in the cauchy case aggregating such models can yield complex dynamics with local and global explosion as well as variation in the rate of explosion the asymptotic behavior of a vector of sample autocorrelations is studied in a semi parametric noncausal ar 1 framework with pareto like tails and diagnostic tests are proposed empirical results based on the nasdaq composite price index are provided

the asymptotic behavior of quadratic forms in φ mixing random variables let z i i 1 be a linear process defined by z email protected j 0 d email protected t j with d j j 0 being a regular varying sequence of real numbers and x t

limit laws for the maximum and minimum of stationary sequences the class of non degenerate joint limiting distributions for the maximum and minimum of stationary mixing sequences is determined these limit distributions are of the form h x h x y where h x y is a bivariate extreme value distribution unlike the classical result for i i d sequences the maximum and minimum of stationary mixing sequences may be asymptotically dependent we also give a sufficient condition for the asymptotic independence of the maximum and minimum finally an example of a stationary sequence satisfying the mixing condition d in leadbetter but which is not weakly mixing is constructed

three level bddc in three dimensions balancing domain decomposition by constraints bddc methods are nonoverlapping iterative substructuring domain decomposition methods for the solution of large sparse linear algebraic systems arising from the discretization of elliptic boundary value problems their coarse problems are given in terms of a small number of continuity constraints for each subdomain which are enforced across the interface the coarse problem matrix is generated and factored by a direct solver at the beginning of the computation and it can ultimately become a bottleneck if the number of subdomains is very large in this paper two three level bddc methods are introduced for solving the coarse problem approximately for problems in three dimensions this is an extension of previous work for the two dimensional case edge constraints are considered in this work since vertex constraints alone which work well in two dimensions result in a noncompetitive algorithm in three dimensions some new technical tools are then needed in the analysis and this makes the three dimensional case more complicated estimates of the condition numbers are provided for two three level bddc methods and numerical experiments are also discussed

alternation with restrictions on looping alternating turing machines with restrictions preventing them from returning to a previous configuration model games with rules enforcing such a restriction for instance the chinese version of go such restrictions do not affect the time complexity of problems for alternating turing machines but space s on a machine with the restriction is equivalent either to time or to space exponential in s on a normal alternating machine depending on the precise nature of the restriction

undirected edge geography abstract the game of edge geography is played by two players who alternately move a token on a graph from one vertex to an adjacent vertex erasing the edge in between the player who first has no legal move is the loser we show that the decision problem of determining whether a position in this game is a win for the first player is pspace complete further the problem remains pspace complete when restricted to planar graphs with maximum degree 3 however if the underlying graph is bipartite we provide 1 a linear algebraic characterization of the p and n positions yielding 2 a polynomial time algorithm for deciding whether any given position is p or n and also 3 a polynomial time algorithm to find winning moves

bddc algorithms for incompressible stokes equations the purpose of this paper is to extend the balancing domain decomposition by constraints bddc algorithm to saddle point problems that arise when mixed finite element methods are used to approximate the system of incompressible stokes equations the bddc algorithms are iterative substructuring methods which form a class of domain decomposition methods based on the decomposition of the domain of the differential equations into nonoverlapping subdomains they are defined in terms of a set of primal continuity constraints which are enforced across the interface between the subdomains and which provide a coarse space component of the preconditioner sets of such constraints are identified for which bounds on the rate of convergence can be established that are just as strong as previously known bounds for the elliptic case in fact the preconditioned operator is effectively positive definite which makes the use of a conjugate gradient method possible a close connection is also established between the bddc

limit theory for the sample covariance and correlation functions of moving averages abstract document describes a moving average process which have regularly varying tail probabilities with index alpha 0 the limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite variance but an infinite fourth moment furthermore in the infinite variance case 0 alpha 2 the sample correlation function is shown to converge in distribution to the ratio of two independent stable random variables with indices alpha and alpha 2 respectively this result immediately gives the limit distribution for the least squares estimates of the parameters in an autoregressive process author

the limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes we investigate the maximum increment of a random walk with heavy tailed jump size distribution here heavy tailedness is understood as regular variation of the finite dimensional distributions the jump sizes constitute a strictly stationary sequence using a continuous mapping argument acting on the point processes of the normalized jump sizes we prove that the maximum increment of the random walk converges in distribution to a frechet distributed random variable

limit theory for moving averages of random variables with regularly varying tail probabilities let z k infty k infty be iid where the z k s have regularly varying tail probabilities under mild conditions on a real sequence c j j geq 0 the stationary process x n sum infty j 0 c jz n j n geq 1 exists a point process based on x n converges weakly and from this a host of weak limit results for functionals of x n ensue we study sums extremes excedences and first passages as well as behavior of sample covariance functions

nested bddc for a saddle point problem we propose a nested bddc for a class of saddle point problems the method solves for both flux and pressure variables the fluxes are resolved in three steps the coarse solve is followed by subdomain solves and last we look for a divergence free flux correction and pressure variables using conjugate gradients with a multilevel bddc preconditioner because the coarse solve in the first step has the same structure as the original problem we can use this procedure recursively and solve a hierarchy of coarse problems only approximately utilizing the coarse problems known from the bddc the resulting algorithm thus first performs several upscaling steps and then solves a hierarchy of problems that have the same structure but increase in size while sweeping down the levels using the same components in the first and in the third step on each level and also reusing the components from the higher levels because the coarsening can be quite aggressive the number of levels can be kept small and the additional computational cost is significantly reduced due to the reuse of the components we also provide the condition number bound and numerical experiments confirming the theory

complexity of path forming games abstract for a number of two player games where players alternately choose the next vertex of a simple or an elementary path in a graph we consider the problem to determine whether for a given game instance there is a winning strategy for the first player we show several of these problems to be pspace complete in some special cases we obtain polynomial time algorithms based on graph rewriting or an intricate form of dynamic programming e g we show generalized geography and some other pspace complete problems to be linear time solvable on graphs with constant bounded treewidth

all structured programs have small tree width and good register allocation the register allocation problem for an imperative program is often modelled as the coloring problem of the interference graph of the control flow graph of the program the interference graph of a flow graph g is the intersection graph of some connected subgraphs of g these connected subgraphs represent the lives or life times of variables so the coloring problem models that two variables with overlapping life times should be in different registers for general programs with unrestricted gotos the interference graph can be any graph and hence we cannot in general color within a factor o n from optimality unless np p

a dual primal feti method for incompressible stokes equations in this paper a dual primal feti method is developed for incompressible stokes equations approximated by mixed finite elements with discontinuous pressures the domain of the problem is decomposed into nonoverlapping subdomains and the continuity of the velocity across the subdomain interface is enforced by introducing lagrange multipliers by a schur complement procedure the solution of an indefinite stokes problem is reduced to solving a symmetric positive definite problem for the dual variables i e the lagrange multipliers this dual problem is solved by the conjugate gradient method with a dirichlet preconditioner in each iteration step both subdomain problems and a coarse level problem are solved by a direct method it is proved that the condition number of this preconditioned dual problem is independent of the number of subdomains and bounded from above by the square of the product of the inverse of the inf sup constant of the discrete problem and the logarithm of the number of unknowns in the individual subdomains numerical experiments demonstrate the scalability of this new method

efficient solution to connectivity problems on hierarchically defined graphs using hierarchical definitions we can describe very large graphs in small spaces in this paper we discuss how such succinct graph descriptions can be used to speed up the solution of graph problems we present the bottom up method that solves graph problems without expanding the hierarchical description this allows solutions that are efficient in terms of the hierarchical graph description instead of the size of the expanded graph we exemplify the method by giving efficient solutions to connectivity problems on hierarchical graphs our results have applications in computer aided design for integrated circuit design and other engineering problems

automatic declustering of rare events the analysis of events with low probability but disastrous impact entails understanding how they cluster in time we present an automatic three step procedure for identifying clusters estimating the cluster size distribution and constructing confidence intervals for the extremal index which measures the degree of clustering of rare events the third step combines empirical likelihood and parametric likelihood approaches simulations show that our new procedure performs very well for finite samples and outperforms previous methods in constructing confidence intervals for the extremal index when there is clustering in the data as well as in estimating probabilities for small clusters copyright 2013 oxford university press

a partial k arboretum of graphs with bounded treewidth the notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies this survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class also some mutual relations between such classes are discussed

modeling of time series arrays by multistep prediction or likelihood methods abstract an estimation theory is provided for the fitting of possibly incorrect invertible short memory models to short or long memory time series or time series arrays by multistep prediction error minimization or gaussian likelihood maximization by array we mean data y t t 1 t t that depend on the number of observations t such as regression or other estimated model residuals or the outputs of time varying filters for example seasonal adjustments our theory only requires the modeled array to have basic properties for a s i p convergence of parameter estimates the array s sample lagged second moments must converge a s i p and its end values y 1 j t and y t j t must be of order less than t 1 2 or an appropriately differenced version of the observed array must have these properties in findley et al ann statist 29 2001 815 broad classes of arrays were shown to have these properties even for the special case of autoregressive moving average models fit to stationary gaussian time series data our result on the convergence of parameter estimates minimizing p step ahead prediction error sums of squares is new

balancing neumann neumann preconditioners for mixed approximations of heterogeneous problems in linear elasticity balancing neumann neumann methods are extented to mixed formulations of the linear elasticity system with discontinuous coefficients discretized with mixed finite or spectral elements with discontinuous pressures these domain decomposition methods implicitly eliminate the degrees of freedom associated with the interior of each subdomain and solve iteratively the resulting saddle point schur complement using a hybrid preconditioner based on a coarse mixed elasticity problem and local mixed elasticity problems with natural and essential boundary conditions a polylogarithmic bound in the local number of degrees of freedom is proven for the condition number of the preconditioned operator in the constant coefficient case parallel and serial numerical experiments confirm the theoretical results indicate that they still hold for systems with discontinuous coefficients and show that our algorithm is scalable parallel and robust with respect to material heterogeneities the results on heterogeneous general problems are also supported in part by our theory

new scaling algorithms for the assignment and minimum mean cycle problems in this paper we suggest new scaling algorithms for the assignment and minimum mean cycle problems our assignment algorithm is based on applying scaling to a hybrid version of the recentauction algorithm of bertsekas and the successive shortest path algorithm the algorithm proceeds by relaxing the optimality conditions and the amount of relaxation is successively reduced to zero on a network with 2n nodes m arcs and integer arc costs bounded byc the algorithm runs in o sqrt n m log nc time and uses very simple data structures this time bound is comparable to the time taken by gabow and tarjan s scaling algorithm and is better than all other time bounds under thesimilarity assumption i e c o nk for somek we next consider the minimum mean cycle problem themean cost of a cycle is defined as the cost of the cycle divided by the number of arcs it contains theminimum mean cycle problem is to identify a cycle whose mean cost is minimum we show that by using ideas of the assignment algorithm in an approximate binary search procedure the minimum mean cycle problem can also be solved in o sqrt n m lognc time under the similarity assumption this is the best available time bound to solve the minimum mean cycle problem

a three level bddc algorithm for mortar discretizations in this paper a three level balancing domain decomposition by constraints bddc algorithm is developed for the solutions of large sparse algebraic linear systems arising from the mortar discretization of elliptic boundary value problems the mortar discretization is considered on geometrically nonconforming subdomain partitions in two level bddc algorithms the coarse problem needs to be solved exactly however its size will increase with the increase of the number of the subdomains to overcome this limitation the three level algorithm solves the coarse problem inexactly while a good rate of convergence is maintained this is an extension of previous work the three level bddc algorithms for standard finite element discretization estimates of the condition numbers are provided for the three level bddc method and numerical experiments are also discussed

ergodic theory abelian groups and point processes induced by stable random fields we consider a point process sequence induced by a stationary symmetric stable 0 2 discrete parameter random field it is easy to prove following the arguments in the one dimensional case in stochastic process appl 114 2004 191 210 that if the random field is generated by a dissipative group action then the point process sequence converges weakly to a cluster poisson process for the conservative case no general result is known even in the one dimensional case we look at a specific class of stable random fields generated by conservative actions whose effective dimensions can be computed using the structure theorem of finitely generated abelian groups the corresponding point processes sequence is not tight and hence needs to be properly normalized in order to ensure weak convergence this weak limit is computed using extreme value theory and some counting techniques

a nonoverlapping domain decomposition method for incompressible stokes equations with continuous pressures a nonoverlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible stokes equations a continuous finite element space for the pressure is used in the proposed algorithm lagrange multipliers are used to enforce continuity of the velocity component across the subdomain boundary the continuity of the pressure component is enforced in the primal form i e neighboring subdomains share the same pressure degrees of freedom on the subdomain interface and no lagrange multipliers are needed after eliminating all velocity variables and the independent subdomain interior parts of the pressures a symmetric positive semidefinite linear system for the subdomain boundary pressures and the lagrange multipliers is formed and solved by a preconditioned conjugate gradient method a lumped preconditioner is studied and the condition number bound of the preconditioned operator is proved to be independent of the number of subdomains fo

feti dp bddc and block cholesky methods the feti dp and bddc algorithms are reformulated using block cholesky factorizations an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations instead of introducing lagrange multipliers to enforce the coarse level primal continuity constraints in these algorithms a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom with the new formulation of these algorithms a simplified proof is provided that the spectra of a pair of feti dp and bddc algorithms with the same set of primal constraints are essentially the same numerical experiments for a two dimensional laplace s equation also confirm this result copyright 2005 john wiley sons ltd