efficient arnoldi type algorithms for rational eigenvalue problems arising in fluid solid systems we develop and analyze efficient methods for computing damped vibration modes of an acoustic fluid confined in a cavity with absorbing walls capable of dissipating acoustic energy the discretization in terms of pressure nodal finite elements gives rise to a rational eigenvalue problem numerical evidence shows that there are no spurious eigenmodes for such discretization and also confirms that the discretization based on nodal pressures is much more efficient than that based on raviart thomas finite elements for the displacement field the trimmed linearization method is used to linearize the associated rational eigenvalue problem into a generalized eigenvalue problem gep of the form ax lbx for solving the gep we apply arnoldi algorithm to two different types of single matrices b 1a and ab 1 numerical accuracy shows that the application of arnoldi on ab 1 is better than that on b 1a

leavitt path algebras are graded von neumann regular rings abstract in sharp contrast to the abrams rangaswamy theorem that the only von neumann regular leavitt path algebras are exactly those associated to acyclic graphs here we prove that the leavitt path algebra of any arbitrary graph is a graded von neumann regular ring several properties of leavitt path algebras such as triviality of the jacobson radical flatness of graded modules and finitely generated graded right left ideals being generated by an idempotent element follow as a consequence of general theory of graded von neumann regular rings

on adaptive estimation in stationary arma processes on demontre la normalite asymptotique locale puis on construit des estimateurs localement asymptotiquement minimax

weighted maximum likelihood for dynamic factor analysis and forecasting with mixed frequency data for the purpose of forecasting key macroeconomic or financial variables from a panel of time series variables we adopt the dynamic factor model and propose a weighted likelihood based method for parameter estimation the loglikelihood function is split into two parts that are weighted differently the first part is associated with the key variables while the second part is associated with the related variables which may contribute to the forecasting of key variables we derive asymptotic properties including consistency and asymptotic normality of the weighted maximum likelihood estimator we show that this estimator outperforms the standard likelihood based estimator in approximating the true unknown distribution of the data as well as in out of sample forecasting accuracy we verify the new estimation method in a monte carlo study and investigate the role of different weights in different settings in the context of forecasting gross domestic product growth this key variable is typically observed at a low quarterly frequency while the supporting variables are observed at a high monthly frequency we adopt a low frequency representation of the mixed frequency dynamic factor model and discuss the computational efficiencies of this approach in our empirical study for the u s economy we present improvements in nowcasting and forecasting accuracy when the weighted likelihood based estimation procedure is adopted

asymptotics for parametric garch in mean models abstract in this paper we develop an asymptotic theory for the quasi maximum likelihood estimator qmle of the parametric garch in mean model the asymptotics is based on a study of the volatility as a process of the model parameters the proof makes use of stochastic recurrence equations for this random function and uses exponential inequalities to localize the problem our results show why the asymptotics for this specification is quite complex although it is a rather standard parametric model nevertheless our theory does not yet treat all standard specifications of the mean function

finite element approximation of a displacement formulation for time domain elastoacoustic vibrations this paper deals with the numerical solution of a system of second order in time partial differential equations modeling the vibrations of a coupling between an elastic solid and an inviscid compressible fluid both media are described in terms of their respective displacement fields the problem is solved in the time domain by combining a newmark s scheme for time discretization with a finite element method for space discretization the latter combines standard lagrangian elements in the solid with lowest order raviart thomas elements in the fluid stability is proved and numerical results showing the good behavior of the method are reported

category equivalences involving graded modules over path algebras of quivers abstract let q be a finite quiver with vertex set i and arrow set q 1 k a field and k q its path algebra with its standard grading this paper proves some category equivalences involving the quotient category qgr k q gr k q fdim k q of graded k q modules modulo those that are the sum of their finite dimensional submodules namely qgr k q mod s q gr l q mod l q 0 qgr k q n here s q lim end k i k q 1 n is a direct limit of finite dimensional semisimple algebras q is the quiver without sources or sinks that is obtained by repeatedly removing all sinks and sources from q l q is the leavitt path algebra of q l q 0 is its degree zero component and q n is the quiver whose incidence matrix is the n th power of that for q it is also shown that all short exact sequences in qgr k q the full subcategory of finitely presented objects in qgr k q split consequently qgr k q can be given the structure of a triangulated category with suspension functor the serre degree twist 1 this triangulated category is equivalent to the singularity category d b d perf where is the radical square zero algebra k q k q 2 and d b is the bounded derived category of finite dimensional left modules

eigenvalue approximation by mixed and hybrid methods note univ maryland dept math college pk md 20742 ecole polytech ctr math appl f 91128 palaiseau france univ paris 6 f 75230 paris 05 france mercier b cea limeil f 94190 villeneuve france isi document delivery no lq584times cited 29cited reference count 44 reference asn article 1981 005doi 10 2307 2007651 record created on 2006 08 24 modified on 2017 05 12

the leavitt path algebra of a graph abstract for any row finite graph e and any field k we construct the leavitt path algebra l e having coefficients in k when k is the field of complex numbers then l e is the algebraic analog of the cuntz krieger algebra c e described in i raeburn graph algebras in cbms reg conf ser math vol 103 amer math soc 2005 the matrix rings m n k and the leavitt algebras l 1 n appear as algebras of the form l e for various graphs e in our main result we give necessary and sufficient conditions on e which imply that l e is simple

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

stable limits of martingale transforms with application to the estimation of garch parameters in this paper we study the asymptotic behavior of the gaussian quasi maximum likelihood estimator of a stationary garch process with heavy tailed innovations this means that the innovations are regularly varying with index 2 2 4 then in particular the marginal distribution of the garch process has infinite fourth moment and standard asymptotic theory with normal limits and p n rates breaks down this was recently observed by hall and yao econometrica 71 2003 285 317 it is the aim of this paper to indicate that the limit theory for the parameter estimators in the heavy tailed case nevertheless very much parallels the normal asymptotic theory in the light tailed case the limit theory is based on the clt for stationary ergodic finite variance martingale difference sequences in the heavy tailed case such a general result does not exist but an analogous result with infinite variance stable limits can be shown to hold under certain mixing conditions which are satisfied for garch processes it is the aim of the paper to give a general structural result for infinite variance limits which can also be applied in situations more general than garch

modelling and numerical solution of elastoacoustic vibrations with interface damping a finite element method is applied to compute the vibrations of an elastoacoustic system subject to an external harmonic excitation the effect of a thin layer of noise damping material between the fluid and the solid is taken into account by relaxing the interface kinematic condition of perfect contact we consider the non linear eigenvalue problem arising from the free vibration problem for the damped system for the case of a fluid in a rectangular rigid cavity with one absorbing wall we deduce the dispersion equation which allows computing analytically its eigenvalues and eigenmodes and compare the numerical solution with them finally we apply the finite element method to assess the effect of introducing a real viscoelastic material to damp the elastoacoustic vibrations of a coupled system copyright 1999 john wiley sons ltd

kalman filtering with random coefficients and contractions the riccati transformation of linear filtering control theory is shown to be a contraction on the space of positive symmetric matrices this is used to describe the asymptotic behavior of the filter for systems with stochastic stationary parameters

whittle estimation of egarch and other exponential volatility models abstract the strong consistency and asymptotic normality of the whittle estimate of the parameters in a class of exponential volatility processes are established our main focus here are the egarch model of nelson d 1991 conditional heteroscedasticity in asset pricing a new approach econometrica 59 347 370 and other one shock models such as the gjr model of glosten l jaganathan r runkle d 1993 on the relation between the expected value and the volatility of the nominal excess returns on stocks journal of finance 48 1779 1801 but two shock models such as the sv model of taylor s 1986 modelling financial time series wiley chichester uk are also comprised by our assumptions the variable of interest might not have finite fractional moment of any order and so in particular finite variance is not imposed we allow for a wide range of degrees of persistence of shocks to conditional variance allowing for both short and long memory

finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics a quadratic eigenvalue problem arising in the determination of the vibration modes of an acoustic fluid contained in a cavity with absorbing walls is considered the problem is shown to be equivalent to the spectral problem for a noncompact operator and a thorough spectral characterization is given a numerical discretization based on raviart thomas finite elements is analyzed the method is proved to be free of spurious modes and to converge with optimal order implementation issues and numerical experiments confirming the theoretical results are reported

quasi maximum likelihood estimation in conditionally heteroscedastic time series a stochastic recurrence equations approach this paper studies the quasi maximum likelihood estimator qmle in a general conditionally heteroscedastic time series model of multiplicative form xt t zt where the unobservable volatility t is a parametric function of xt 1 x t p t 1 t q for some p q 0 and zt is standardized i i d noise we assume that these models are solutions to stochastic recurrence equations which satisfy a contraction random lipschitz coefficient property these assumptions are satisfied for the popular garch asymmetric garch and exponential garch processes exploiting the contraction property we give conditions for the existence and uniqueness of a strictly stationary solution xt to the stochastic recurrence equation and establish consistency and asymptotic normality of the qmle we also discuss the problem of invertibility of such time series models 1 introduction gaussian quasi maximum likelihood estimation that is likelihood estimation under the hypothesis of gaussian innovations is a popular method which is widely used for inference in time series models however it is often a nontrivial task to establish the consistency and asymptotic normality of the quasi maximum likelihood estimator qmle applied to specific models and therefore an in depth analysis of the probabilistic structure generated by the model is called for a classical example of this kind is the seminal paper by hannan 18 on estimation in linear arma time series in this paper we study the qmle for a general class of conditionally heteroscedastic time series models which includes garch asymmetric garch and exponential garch recall that a garch p q generalized autoregressive conditionally heteroscedastic of order p q process 4 i s def ined by

finite element vibration analysis of fluid solid systems without spurious modes this paper deals with the finite element approximation of the vibration modes of a problem with fluid structure interaction displacement variables are used for both the fluid and the solid to avoid the typical spurious modes of this formulation we introduce a nonconforming discretization error estimates for the approximation of eigenvalues and eigenvectors are given

approximation of eigenvalues in mixed form discrete compactness property and application to hp mixed finite elements abstract in this paper we discuss the discrete compactness property dcp which is a well known tool for the analysis of finite element approximations of maxwell s eigenvalues we restrict our presentation to maxwell s eigenvalues but the theory applies to more general situations and in particular to mixed finite element schemes that can be written in the framework of de rham complex and which enjoy suitable compactness properties we investigate the relationships between dcp and standard mixed conditions for the good approximation of eigenvalues as a consequence of our theory the convergence analysis of the rectangular hp version of raviart thomas finite elements for the approximation of laplace eigenvalues is presented as a corollary of the analogous result for hp edge elements applied to the approximation of maxwell s eigenvalues d boffi m costabel m dauge l demkowicz discrete compactness for the hp version of rectangular edge finite elements siam j numer anal 44 3 2006 979 1004

what is a linear process abstract we argue that given even an infinitely long data sequence it is impossible with any test statistic to distinguish perfectly between linear and nonlinear processes including slightly noisy chaotic processes our approach is to consider the set of moving average linear processes and study its closure under a suitable metric we give the precise characterization of this closure which is unexpectedly large containing nonergodic processes which are poisson sums of independent and identically distributed copies of a stationary process proofs of these results will appear elsewhere

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

spectral approximation of variationally posed eigenvalue problems by nonconforming methods this paper deals with the nonconforming spectral approximation of variationally posed eigenvalue problems it is an extension to more general situations of known previous results about nonconforming methods as an application of the present theory convergence and optimal order error estimates are proved for the lowest order crouzeix raviart approximation of the eigenpairs of two representative second order elliptical operators

least absolute deviation estimation for all pass time series models an autoregressive moving average model in which all of the roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all pass time series model all pass models generate uncorrelated white noise time series but these series are not independent in the non gaussian case an approximation to the likelihood of the model in the case of laplacian two sided exponential noise yields a modified absolute deviations criterion which can be used even if the underlying noise is not laplacian asymptotic normality for least absolute deviation estimators of the model parameters is established under general conditions behavior of the estimators in finite samples is studied via simulation the methodology is applied to exchange rate returns to show that linear all pass models can mimic nonlinear behavior and is applied to stock market volume data to illustrate a two step procedure for fitting noncausal autoregressions

reduced models for modal analysis of fluid structure systems taking into account compressibility and gravity effects abstract it is proposed to investigate and discuss from theoretical point of view various reduced order variational formulations for modal analysis of linear vibrations of bounded fluid structure systems with free surface taking into account possible gravity compressibility interactions in a non homogeneous fluid situation those formulations are based on substructural synthesis techniques and various modal reduction schemes are then obtained in a previous paper various original formulations have been exhibited associated to numerical validation the present paper starts from those formulations in order to construct theoretically various reduced order models

risk parameter estimation in volatility models abstract this paper introduces the concept of risk parameter in conditional volatility models of the form t t 0 t and develops statistical procedures to estimate this parameter for a given risk measure r the risk parameter is expressed as a function of the volatility coefficients 0 and the risk r t of the innovation process a two step method is proposed to successively estimate these quantities an alternative one step approach relying on a reparameterization of the model and the use of a non gaussian qml is proposed asymptotic results are established for smooth risk measures as well as for the value at risk var asymptotic comparisons of the two approaches for var estimation suggest a superiority of the one step method when the innovations are heavy tailed for standard garch models the comparison only depends on characteristics of the innovations distribution not on the volatility parameters monte carlo experiments and an empirical study illustrate the superiority of the one step approach for financial series

a posteriori error estimates in finite element acoustic analysis we present an a posteriori error estimator for the approximations of the acoustic vibration modes obtained by a finite element method which does not present spurious or circulation modes for non zero frequencies we prove that the proposed estimator is equivalent to the error in the approximation of the eigenvectors up to higher order terms with constants independent of the eigenvalues numerical results for some test examples are presented which show the good behavior of the estimator when it is used as local error indicator for adaptive refinement

finite element analysis of compressible and incompressible fluid solid systems this paper deals with a finite element method to solve interior fluid structure vibration problems valid for compressible and incompressible fluids it is based on a displacement formulation for both the fluid and the solid the pressure of the fluid is also used as a variable for the theoretical analysis yielding a well posed mixed linear eigenvalue problem lowest order triangular raviart thomas elements are used for the fluid and classical piece wise linear elements for the solid transmission conditions at the fluid solid interface are taken into account in a weak sense yielding a nonconforming discretization the method does not present spurious or circulation modes for nonzero frequencies convergence is proved and error estimates independent of the acoustic speed are given for incompressible fluids a convenient equivalent stream function formulation and a post process to compute the pressure are introduced

beta negative binomial auto regressions for modelling integer valued time series with extreme observations the paper introduces a general class of heavy tailed auto regressions for modelling integer valued time series with outliers the specification proposed is based on a heavy tailed mixture of negative binomial distributions that features an observation driven dynamic equation for the conditional expectation the existence of a stationary and ergodic solution for the class of auto regressive processes is shown under general conditions the estimation of the model can be easily performed by maximum likelihood given the closed form of the likelihood function the strong consistency and the asymptotic normality of the estimator are formally derived two examples of specifications illustrate the flexibility of the approach and the relevance of the theoretical results in particular a linear dynamic equation and a score driven equation for the conditional expectation are studied the score driven specification is shown to be particularly appealing as it delivers a robust filtering method that attenuates the effect of outliers empirical applications to the series of narcotics trafficking reports in sydney and the euro pound sterling exchange rate illustrate the effectiveness of the method in handling extreme observations

finite element solution of incompressible fluid structure vibration problems in this paper we solve an eigenvalue problem arising from the computation of the vibrations of a coupled system incompressible fluid elastic structure in absence of external forces we use displacement variables for both the solid and the fluid but the fluid displacements are written as curls of a stream function classical linear triangular finite elements are used for the solid displacements and for the stream function in the fluid the kinematic transmission conditions at the fluid solid interface are taken into account in a weak sense by means of a lagrange multiplier the method does not present spurious or circulation modes for non zero frequencies numerical results are given for some test cases 1997 by john wiley sons ltd

semigroup crossed products and the toeplitz algebras of nonabelian groups abstract we consider the quasi lattice ordered groups g p recently introduced by nica we realise their universal toeplitz algebra as a crossed product b p p by a semigroup of endomorphisms and show that the toeplitz representation is faithful precisely when an amenability condition is satisfied we then show directly that many interesting free products are amenable the final result contains theorems of cuntz and dinh on the uniqueness of toeplitz cuntz algebras as special cases

a parametric study on fluid structure interaction problems abstract this paper deals with finite element analysis of the fluid structure systems considering the coupled effect of elastic structure and fluid the equations of motion of the fluid considered inviscid and compressible are expressed in terms of the pressure variable alone the elastic structure and the fluid domain are treated as two separate systems and discretized with finite elements the solution of the coupled system is accomplished by solving the two systems separately with the interaction effects at the fluid solid interface enforced by a developed iterative scheme non divergent pressure and displacement are obtained simultaneously through a few numbers of iterations studies show the accuracy of the proposed algorithm while comparing with the existing ones available in the literature the parametric study of the coupled system shows the importance of fluid height and material property of the structure

finite element spectral analysis for the mixed formulation of the elasticity equations the aim of this paper is to analyze the linear elasticity eigenvalue problem formulated in terms of the stress tensor and the rotation this is achieved by considering a mixed variational formulation in which the symmetry of the stress tensor is imposed weakly we show that a discretization of the mixed eigenvalue elasticity problem with reduced symmetry based on the lowest order arnold falk winther element provides a correct approximation of the spectrum we also prove quasi optimal error estimates finally we report some numerical experiments

fractional skew monoid rings abstract given an action of a monoid t on a ring a by ring endomorphisms and an ore subset s of t a general construction of a fractional skew monoid ring s op a t is given extending the usual constructions of skew group rings and of skew semigroup rings in case s is a subsemigroup of a group g such that g s 1s we obtain a g graded ring s op a s with the property that for each s s the s component contains a left invertible element and the s 1 component contains a right invertible element in the most basic case where g z and s t z the construction is fully determined by a single ring endomorphism of a if is an isomorphism onto a proper corner pap we obtain an analogue of the usual skew laurent polynomial ring denoted by a t t examples of this construction are given and it is proven that several classes of known algebras including the leavitt algebras of type 1 n can be presented in the form a t t finally mild and reasonably natural conditions are obtained under which s op a s is a purely infinite simple ring

finite element analysis of the vibration problem of a plate coupled with a fluid we consider the approximation of the vibration modes of an elastic plate in contact with a compressible fluid the plate is modelled by reissner mindlin equations while the fluid is described in terms of displacement variables this formulation leads to a symmetric eigenvalue problem reissner mindlin equations are discretized by a mixed method the equations for the fluid with raviart thomas elements and a non conforming coupling is used on the interface in order to prove that the method is locking free we consider a family of problems one for each thickness t 0 and introduce appropriate scalings for the physical parameters so that these problems attain a limit when t to 0 we prove that spurious eigenvalues do not arise with this discretization and we obtain optimal order error estimates for the eigenvalues and eigenvectors valid uniformly on the thickness parameter t finally we present numerical results confirming the good performance of the method

accurate pressure post process of a finite element method for elastoacoustics this paper deals with a post process to obtain a more accurate approximation of the fluid pressure from a finite element computation of the vibration modes of a fluid structure coupled system the underlying finite element method based on a displacement formulation for both media consists of using raviart thomas elements for the fluid combined with standard continuous elements for the solid an easy to compute post process of the pressure is derived the relation between this post process and an alternative finite element approximation of the problem based on discretizing the fluid pressure by enriched crouzeix raviart elements is studied higher order estimates for the l2 norm of the post processed pressure are proved by exploiting this relation as a by product higher order l2 estimates for the solid displacements obtained with the original method are also proved

large deviations and ruin probabilities for solutions to stochastic recurrence equations with heavy tailed innovations in this paper we consider the stochastic recurrence equation y t a t y t 1 b t for an i i d sequence of pairs a t b t of nonnegative random variables where we assume that b t is regularly varying with index k 0 and ea k t x c 1 np y 1 x as x holds for some constant c 1 0 for k 1 we also study the large deviation probabilities p s n es n x x x n for some sequence x n whose growth depends on the heaviness of the tail of the distribution of y 1 we show that the relation p s n es n x c 2 np y 1 x holds uniformly for x x n and some constant c 2 0 then we apply the large deviation results to derive bounds for the ruin probability u p sup n 1 s n es n n u for any 0 we show that u c 3 up y 1 u 1 1 1 for some constant c 3 0 in contrast to the case of i i d regularly varying y t s when the above results hold with c 1 c 2 c 3 1 the constants c 1 c 2 and c 3 are different from 1

classification of certain infinite simple c algebras the class of c algebras that arise as the crossed product of a stable simple af algebra with a z action determined by an automorphism which maps a projection in the algebra onto a proper subprojection is proved to consist of simple purely infinite c algebras and a specific subclass of it is proved to be classified by k theory this subclass is large enough to exhaust all possible k groups if g0 and g1 are countable abelian groups with g1 torsion free as it must be then there is a c algebras a in the classified subclass with k0 a g0 and k 1 a g1 the subclass contains the cuntz algebras o with n even and the cuntz krieger algebras o a with k0 o a of finite old order and it is closed under forming inductive limits the c algebras in the classified subclass can be viewed as classifiable models in a strong sense of general simple purely infinite c algebras with the same k theory

semiparametric inference in a garch in mean model abstract a new semiparametric estimator for an empirical asset pricing model with general nonparametric risk return tradeoff and garch type underlying volatility is introduced based on the profile likelihood approach it does not rely on any initial parametric estimator of the conditional mean function and it is under stated conditions consistent asymptotically normal and efficient i e it achieves the semiparametric lower bound a sampling experiment provides finite sample comparisons with the parametric approach and the iterative semiparametric approach with parametric initial estimate of conrad and mammen 2008 an application to daily stock market returns suggests that the risk return relation is indeed nonlinear

modelling volatility by variance decomposition abstract in this paper we propose two parametric alternatives to the standard gjr garch model of glosten et al 1993 based on additive and multiplicative decompositions of the variance they allow the variance of the model to have a smooth time varying structure the suggested parameterizations describe structural change in the conditional and unconditional variances where the transition between regimes over time is smooth the main focus is on the multiplicative decomposition of the variance into an unconditional and conditional components estimation of the multiplicative model is discussed in detail an empirical application to daily stock returns illustrates the functioning of the model the results show that the long memory type behaviour of the sample autocorrelation functions of the absolute returns can also be explained by deterministic changes in the unconditional variance

asymptotic normality of the quasi maximum likelihood estimator for multidimensional causal processes strong consistency and asymptotic normality of the quasi maximum likelihood estimator qmle are given for a general class of multidimensional causal processes for particular cases already studied in the literature for instance univariate or multivariate garch arch arma garch processes the assumptions required for establishing these results are often weaker than existing conditions the qmle asymptotic behavior is also given for numerous new examples of univariate or multivariate processes for instance tarch or nlarch processes

numerical solution of the acoustic wave equation using raviart thomas elements in this paper we discuss the numerical approximation of the displacement form of the acoustic wave equation using mixed finite elements the mixed formulation allows for approximation of both displacement and pressure at each time step without the need for post processing lowest order and next to lowest order raviart thomas elements are used for the spatial discretization and centered finite differences are used to advance in time use of these raviart thomas elements results in a diagonal mass matrix for resolution of pressure and a mass matrix for the displacement variable that is sparse with a simple structure convergence results for a model problem are provided as are numerical results for a two dimensional problem with a point source

optimal predictions of powers of conditionally heteroscedastic processes in conditionally heteroskedastic models the optimal prediction of powers or logarithms of the absolute process has a simple expression in terms of the volatility process and an expectation involving the independent process a standard procedure for estimating this prediction is to estimate the volatility by gaussian quasi maximum likelihood qml in a first step and to use empirical means based on rescaled innovations to estimate the expectation in a second step this paper proposes an alternative one step procedure based on an appropriate non gaussian qml estimation of the model and establishes the asymptotic properties of the two approaches their performances are compared for finite order garch models and for the infinite arch for the standard garch p q and the asymmetric power garch p q it is shown that the are of the estimators only depends on the prediction problem and some moments of the independent process an application to indexes of major stock exchanges is proposed

convergence of gaussian quasi likelihood random fields for ergodic levy driven sde observed at high frequency this paper investigates the gaussian quasi likelihood estimation of an exponentially ergodic multidimensional markov process which is expressed as a solution to a levy driven stochastic differential equations whose coefficients are supposed to be known except for the finite dimensional parameters to be estimated we suppose that the process is observed under the condition for the rapidly increasing experimental design by means of the polynomial type large deviation inequality the mighty convergence of the corresponding statistical random fields is derived which especially leads to the asymptotic normality at rate p nhn for all the target parameters and also to the convergence of their moments in our results the diffusion coefficient may be degenerate or even null although the resulting estimator is not asymptotically efficient in the presence of jumps we do not require any specific form of the driving levy measure rendering that the proposed estimation procedure is practical and somewhat robust to underlying model specification

a note on the isomorphism conjectures for leavitt path algebras abstract we relate two conjectures which have been raised for classification of leavitt path algebras for purely infinite simple unital leavitt path algebras it is conjectured that k 0 classifies them completely abrams et al 2008 2011 3 4 for arbitrary unital leavitt path algebras it is conjectured that k 0 gr classifies them completely hazrat in press 12 we show that for two finite graphs with no sinks which their associated leavitt path algebras include the purely infinite simple ones if their k 0 gr groups of their leavitt path algebras are isomorphic then their k 0 groups are isomorphic as well we also provide a short proof of the fact that for a finite graph its associated leavitt path algebra is strongly graded if and only if the graph has no sinks

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

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

a virtual element method for the acoustic vibration problem we analyze in this paper a virtual element approximation for the acoustic vibration problem we consider a variational formulation relying only on the fluid displacement and propose a discretization by means of mathrm h mathrm div h div virtual elements with vanishing rotor under standard assumptions on the meshes we show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates with this end we prove approximation properties of the proposed virtual elements we also report some numerical tests supporting our theoretical results

approximation of the buckling problem for reissner mindlin plates this paper deals with the approximation of the buckling coefficients and modes of a clamped plate modeled by the reissner mindlin equations these coefficients are the reciprocals of the eigenvalues of a noncompact operator we give a spectral characterization of this operator and show that the relevant buckling coefficients correspond to isolated nondefective eigenvalues then we consider the numerical computation of these coefficients and their corresponding modes for the finite element approximation of reissner mindlin equations it is well known that some kind of reduced integration or mixed interpolation has to be used to avoid locking in particular we consider duran liberman elements which have been already proved to be locking free for load and vibration problems we adapt the classical approximation theory for noncompact operators to obtain optimal order error estimates for the eigenfunctions and a double order for the eigenvalues these estimates are valid with constants independent of the plate thickness we report some numerical experiments confirming the theoretical results finally we refine the analysis in the case of a uniformly compressed plate

vibration analysis of fluid solid systems using a finite element displacement formulation this report presents a finite element solution for the vibration interaction between an inviscid fluid and a solid the equation of motion governing the inviscid fluid is expressed in terms of the displacements reduced integration is used when computing the element stiffness matrix contributed by the fluid in addition a projection is used on the element mass matrix in order to remove the spurious modes which result from the use of reduced integration

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

finite element analysis of pressure formulation of the elastoacoustic problem in this paper we analyze the non symmetric pressure displacement formulation of the elastoacoustic vibration problem and show its equivalence with the symmetric stiffness coupling formulation we introduce discretizations for these problems based on lagrangian finite elements we show that both formulations are also equivalent at discrete level and prove optimal error estimates for eigenfunctions and eigenvalues both formulations are rewritten such as to be solved with a standard matlab eigensolver we report numerical results comparing the efficiency of the methods over some test examples

the order of convergence of eigenfrequencies in finite element approximations of fluid structure interaction problems in this paper we prove a double order for the convergence of eigenfrequencies in fluid structure vibration problems we improve estimates given recently for compressible and incompressible fluids to do this we extend classical results on finite element spectral approximation to nonconforming methods for noncompact operators

finite element approximation of spectral acoustic problems on curved domains this paper deals with the finite element approximation of the displacement formulation of the spectral acoustic problem on a curved non convex two dimensional domain convergence and error estimates are proved for raviart thomas elements on a discrete polygonal domain h inline equation in the framework of the abstract spectral approximation theory similar results have been previously proved only for polygonal domains numerical tests confirming the theoretical results are reported

error estimates for raviart thomas interpolation of any order on anisotropic tetrahedra we prove optimal order error estimates for the raviart thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition namely the so called three dimensional maximum angle condition and the regular vertex property for tetrahedra our techniques are different from those used in previous papers on the subject and the results obtained are more general in several aspects first intermediate regularity is allowed that is for the raviart thomas interpolation of degree k 0 we prove error estimates of order j 1 when the vector field being approximated has components in w j 1 p for triangles or tetrahedra where 0 j k and 1 p these results are new even in the two dimensional case indeed the estimate was known only in the case j k on the other hand in the three dimensional case results under the maximum angle condition were known only for k 0

simple cuntz pimsner rings abstract necessary and sufficient conditions for when every non zero ideal in a relative cuntz pimsner ring contains a non zero graded ideal when a relative cuntz pimsner ring is simple and when every ideal in a relative cuntz pimsner ring is graded are given a cuntz krieger uniqueness theorem for relative cuntz pimsner rings is also given and condition l and condition k for relative cuntz pimsner rings are introduced as applications of these results a uniqueness result for the toeplitz algebra of a directed graph and characterizations of when crossed products of a ring by a single automorphism and fractional skew monoid rings of a single corner isomorphism are simple are obtained

non simple purely infinite rings in this paper we introduce the concept of purely infinite rings which in the simple case agrees with the already existing notion of pure infiniteness we establish various permanence proper ties of this notion with respect to passage to matrix rings corners and behaviour under extensions so being purely infinite is preserved under morita equivalence we show that a wealth of examples falls into this class including important analogues of constructions commonly found in operator al gebras in particular for any s unital k algebra having enough nonzero idempotents for example for a von neumann regular algebra its tensor product over k with many non simple leavitt path algebras is purely infinite introduction the notion of pure infiniteness has proved key in the the ory of operator algebras since its conception in the early eighties by j cuntz see 27 this was done for simple algebras and provided a huge list of exam ples one of the milestones of the theory became the classification of separable nuclear unital purely infinite simple algebras by means of k theoretic invariants due to kirchberg 41 and phillips 58

multivariate contemporaneous threshold autoregressive models this paper proposes a contemporaneous threshold multivariate smooth transition autoregressive c mstar model in which the regime weights depend on the ex ante probabilities that latent regime specific variables exceed certain threshold values a key feature of the model is that the transition function depends on all the parameters of the model as well as on the data since the mixing weights are also a function of the regime specific noise covariance matrix the model can account for contemporaneous regime specific co movements of the variables the stability and distributional properties of the proposed model are discussed as well as issues of estimation testing and forecasting the practical usefulness of the c mstar model is illustrated by examining the relationship between us stock prices and interest rates

simulated likelihood estimators for discretely observed jump diffusions abstract this paper develops an unbiased monte carlo approximation to the transition density of a jump diffusion process with state dependent drift volatility jump intensity and jump magnitude the approximation is used to construct a likelihood estimator of the parameters of a jump diffusion observed at fixed time intervals that need not be short the estimator is asymptotically unbiased for any sample size it has the same large sample asymptotic properties as the true but uncomputable likelihood estimator numerical results illustrate its properties

z graded rings as cuntz pimsner rings abstract given a z graded ring a and a subring r a it is natural to ask whether a can be realised as the cuntz pimsner ring of some r system in this paper we derive sufficient conditions on a and r for this to be the case as an application we give conditions under which the steinberg algebra a k g associated to a z graded groupoid g n z g n can be realised as the cuntz pimsner ring of an a k g 0 system

pseudo maximum likelihood estimation of arch models strong consistency and asymptotic normality of the gaussian pseudo maximum likelihood estimate of the parameters in a wide class of arch 1 processes are established we require the arch weights to decay at least hyperbolically with a faster rate needed for the central limit theorem than for the law of large numbers various rates are illustrated in examples of particular parameteriza tions in which our conditions are shown to be satis ed

topological aperiodicity for product systems over semigroups of ore type we prove a version of uniqueness theorem for cuntz pimsner algebras of discrete product systems over semigroups of ore type to this end we introduce doplicher roberts picture of cuntz pimsner algebras and the semigroup dual to a product system of regular c correspondences under a certain aperiodicity condition on the latter we obtain the uniqueness theorem and a simplicity criterion for the algebras in question these results generalize the corresponding ones for crossed products by discrete groups due to archbold and spielberg and for exel s crossed products due to exel and vershik they also give interesting conditions for topological higher rank graphs and p graphs and apply to the new cuntz c algebra qn arising from the ax b semigroup over n

analysis of a finite element method for pressure potential formulation of elastoacoustic spectral problems a finite element method to approximate the vibration modes of a structure enclosing an acoustic fluid is analyzed the fluid is described by using simultaneously pressure and displacement potential variables whereas displacement variables are used for the solid a mathematical analysis of the continuous spectral problem is given the problem is discretized on a simplicial mesh by using piecewise constant elements for the pressure and continuous piecewise linear finite elements for the other fields error estimates are settled for approximate eigenvalues and eigenfrequencies finally implementation issues are discussed

finite element computation of the vibration modes of a fluid solid system abstract in this paper we solve the interior elastoacoustic problem by a finite element method which does not present spurious or circulation modes for nonzero frequencies it consists of classical triangular lagrangian elements for the solid and lowest order triangular raviart thomas elements for the fluid transmission conditions at the fluid solid interface are taken into account in a weak sense numerical results for some test examples are presented which show the good performance of the proposed methodology

finite element analysis for a pressure stress formulation of a fluid structure interaction spectral problem the aim of this paper is to analyze an elastoacoustic vibration problem employing a dual mixed formulation in the solid domain the cauchy stress tensor and the rotation are the primary variables in the elastic structure while the standard pressure formulation is considered in the acoustic fluid the resulting mixed eigenvalue problem is approximated by a conforming galerkin scheme based on the lowest order lagrange and arnold falk winther finite element subspaces in the fluid and solid domains respectively we show that the scheme provides a correct approximation of the spectrum and prove quasi optimal error estimates finally we report some numerical experiments

algebraic cuntz pimsner rings from a system consisting of a ring r ap air ofr bimodules q and p and an r bimodule homomorphism p q r we construct a z graded ring t p q called the toeplitz ring and for certain systems a z graded quotient o p q of t p q called the cuntz pimsner ring these rings are the algebraic analogues of the toeplitz c algebra and the cuntz pimsner c algebra associated to a c correspondence also called a hilbert bimodule this new construction generalizes for example the algebraic crossed product by a single automorphism fractional skew monoid rings by a single corner automorphism and leavitt path algebras we also describe the structure of the graded ideals of our graded rings in terms of pairs of ideals of the coefficient ring and show that our cuntz pimsner rings satisfy the graded uniqueness theorem

chasing volatility a persistent multiplicative error model with jumps abstract persistence and unpredictable large increments characterize the volatility of financial returns we propose the multiplicative error model with volatility jumps mem j to describe and predict the probability and the size of these extreme events under the mem j the conditional density of the realized measure is a countably infinite mixture of gamma and kappa distributions with closed form conditional moments we derive stationarity conditions and the asymptotic theory for the maximum likelihood estimation estimates of the volatility jump component confirm that the probability of jumps dramatically increases during the financial crises the mem j improves over other models with fat tails

on the spurious solutions in the high order finite difference methods for eigenvalue problems in this paper the origins of spurious solutions occurring in the high order finite difference methods are studied based on a uniform mesh spurious modes are found in the high order one sided finite difference discretizations of many eigenvalue problems spurious modes are classified as spectral pollution and non spectral pollution the latter can be partially avoided by mesh refinement while the former persists when the mesh is refined through numerical studies of some prototype eigenvalue problems such as those of the helmholtz and beam equations we show that perfect central differentiation schemes do not produce any spurious modes nevertheless high order central difference schemes encounter difficulties in implementing complex boundary conditions we further show that the central difference schemes will produce spurious modes as well if asymmetric approximation is involved in boundary treatments in general central difference schemes are less likely to produce spurious modes than one sided difference schemes 2007 elsevier b v all rights reserved

stationarity of garch processes and of some nonnegative time series abstract two time series models are considered garch processes and generalized multivariate autoregressive equations x n 1 a n 1 x n b n 1 with nonnegative i i d coefficients in each case a necessary and sufficient condition ensuring the existence of a strictly stationary solution is given

theoretical results on fractionally integrated exponential generalized autoregressive conditional heteroskedastic processes abstract here we present a theoretical study on the main properties of fractionally integrated exponential generalized autoregressive conditional heteroskedastic fiegarch processes we analyze the conditions for the existence the invertibility the stationarity and the ergodicity of these processes we prove that if x t t z is a fiegarch p d q process then under mild conditions ln x t 2 t z is an arfima q d 0 with correlated innovations that is an autoregressive fractionally integrated moving average process the convergence order for the polynomial coefficients that describes the volatility is presented and results related to the spectral representation and to the covariance structure of both processes ln x t 2 t z and ln t 2 t z are discussed expressions for the kurtosis and the asymmetry measures for any stationary fiegarch p d q process are also derived the h step ahead forecast for the processes x t t z ln t 2 t z and ln x t 2 t z are given with their respective mean square error of forecast the work also presents a monte carlo simulation study showing how to generate estimate and forecast based on six different fiegarch models the forecasting performance of six models belonging to the class of autoregressive conditional heteroskedastic models namely arch type models and radial basis models is compared through an empirical application to brazilian stock market exchange index