β expectation and β content tolerance limits for balanced one way anova random model this article discusses procedures for computing tolerance limits for a population consisting of many batches the results of mee and owen 1983 for one sided content tolerance limits are extended to the two sided case in addition expectation tolerance limit procedures are presented the procedures given for the case in which the ratio of the between and within variances is known are exact whereas the procedures derived for settings in which the ratio is unknown involve an approximation

computing gaussian likelihoods and their derivatives for general linear mixed models algorithms are described for computing the gaussian likelihood or restricted likelihood corresponding to a general linear mixed model included are arbitrary covariance structures for both the random effects and errors formulas are also given for the first and second derivatives of the likelihoods thus enabling a newton raphson implementation the algorithms make heavy use of the cholesky decomposition the sweep operator and the w transformation also described are the modifications needed for variance profiling fisher scoring and mivque 0 as well as the computational order of the procedures

one sided tolerance limits for balanced and unbalanced random effects models a simple analytical approach for constructing one sided content confidence tolerance limits is proposed for general random effects models with normal data in both balanced and unbalanced data scenarios the approach is based on an approximation to the noncentral t distribution and modified large sample methods for constructing confidence bounds on functions of variance components an alternative bootstrap adjusted limit is also proposed the performance of the analytical and bootstrap adjusted limits is assessed via simulation techniques the results indicate that the analytical limit is generally somewhat conservative but is often less conservative than an existing analytical approach and may provide substantially shorter interval lengths particularly for smaller sample sizes and larger values of the bootstrap adjusted limit generally maintains the nominal confidence level and yields shorter interval lengths though it can be anticonservative for small sample sizes this article has supplementa

a direct approach to conformational dynamics based on hybrid monte carlo recently a novel concept for the computation ofessentialfeatures of the dynamics of hamiltonian systems such as molecular dynamics has been proposed the realization of this concept had been based on subdivision techniques applied to the frobenius perron operator for the dynamical system the present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework this approach allows us to define the phrase conformation in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations in a first step the frequency of conformational changes is characterized in statistical terms leading to the definition of some markov operatortthat describes the corresponding transition probabilities within the canonical ensemble in a second step a discretization oftvia specific hybrid monte carlo techniques is shown to lead to astochasticmatrixp with these theoretical preparaions an identification algorithm for conformations to be presented in a later paper is applicable it is demonstrated that the discretization oftcan be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked numerical results for the n pentane molecule and the triribonucleotide adenylyl 3 5 cytidylyl 3 5 cytidin are given and interpreted

the estimation of the mean squared error of small area estimators abstract small area estimation has received considerable attention in recent years because of a growing demand for reliable small area statistics the direct survey estimators based only on the data from a given small area or small domain are likely to yield unacceptably large standard errors because of small sample size in the domain therefore alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency these estimators use models either implicitly or explicitly that connect the small areas through supplementary e g census and administrative data for example simple synthetic estimators are based on implicit modeling in this article three small area models of battese harter and fuller 1988 dempster rubin and tsutakawa 1981 and fay and herriot 1979 are investigated these models are all special cases of a general mixed linear model involving fixed and random effects and a small area mean can be expr

existence uniqueness and regularity of solutions to systems of nonlocal obstacle problems related to optimal switching we study viscosity solutions to a system of nonlinear degenerate parabolic partial integrodi erential equations with interconnected obstacles this type of problem occurs in the context of optimal

small sample inference for fixed effects from restricted maximum likelihood restricted maximum likelihood reml is now well established as a method for estimating the parameters of the general gaussian linear model with a structured covariance matrix in particular for mixed linear models conventionally estimates of precision and inference for fixed effects are based on their asymptotic distribution which is known to be inadequate for some small sample problems in this paper we present a scaled wald statistic together with an f approximation to its sampling distribution that is shown to perform well in a range of small sample settings the statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias this approach has the advantage that it reproduces both the statistics and f distributions in those settings where the latter is exact namely for hotelling t2 type statistics and for analysis of variance f ratios the performance of the modified statistics is assessed through simulation studies of four different reml analyses and the methods are illustrated using three examples

approximation schemes for viscosity solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of applications including the calculus of variations control theory and differential games recently m g crandall and p l lions established the correct notion of generalized solutions for these equations this article discusses the convergence of general approximation schemes to this solution and gives under certain hypotheses explicit error estimates these results are then applied to obtain various representations as limits of solutions of general explicit and implicit finite difference schemes with error estimates

a priori estimates of smoothness of solutions to difference bellman equations with linear and quasi linear operators a priori estimates for finite difference approximations for the first and second order derivatives are obtained for solutions of parabolic equations described in the title

duality based a posteriori error estimates for some approximation schemes for optimal investment problems abstract we consider a markov chain approximation scheme for utility maximization problems in continuous time which uses in turn a piecewise constant policy approximation euler maruyama time stepping and a gaus hermite approximation of the gausian increments the error estimates previously derived in picarelli and reisinger 2018 are asymmetric between lower and upper bounds due to the control approximation and improve on known results in the literature in the lower case only in the present paper we use duality results to obtain a posteriori upper error bounds which are empirically of the same order as the lower bounds the theoretical results are confirmed by our numerical tests

optimal convergence rate of the explicit finite difference scheme for american option valuation an optimal convergence rate o dx for an explicit finite difference scheme for a variational inequality problem is obtained under the stability condition s email protected dx 2 1 using completely pde methods as a corollary a binomial tree scheme of an american put option where s email protected dx 2 1 is convergent unconditionally with the rate o dt 1 2

a multidimensional exponential utility indifference pricing model with applications to counterparty risk this paper considers exponential utility indifference pricing for a multidimensional nontraded assets model subject to intertemporal default risk and provides a semigroup approximation for the utility indifference price the key tool is the splitting method whose convergence is proved based on the barles souganidis monotone scheme and the convergence rate is derived based on krylov s shaking the coefficients technique we apply our methodology to study the counterparty risk of derivatives in incomplete markets

on uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic pde s we prove several comparison and existence theorems for viscosity solutions of fully nonlinear degenerate elliptic equations one of them extends some recent uniqueness results by jensen some establish the uniqueness of solutions for second order isaacs equations and hence include the uniqueness results for bellman equations by p l lions our comparison results apply even for discontinuous solutions and so perron s method readily yields the existence of continuous solutions

optimal switching for ordinary differential equations we consider the problem of controlling an ordinary differential equation subject to positive switching costs and show in particular that the value functions form the viscosity solution cf 6 7 of the dynamic programming quasi variational inequalities this interpretation allows for a rigorous application of various dynamic programming techniques

error bounds for monotone approximation schemes for parabolic hamilton jacobi bellman equations we obtain nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation numerical schemes for parabolic hamilton jacobi bellman equations by introducing a new notion of consistency our results are robust and general they improve and extend earlier results by krylov barles and jakobsen we apply our general results to various schemes including crank nicholson type finite difference schemes splitting methods and the classical approximation by piecewise constant controls in the first two cases our results are new and in the last two cases the results are obtained by a new method which we develop here

two approximations of solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of application including the calculus of variations control theory and differential games the associated initial value problems almost never have global time classical solutions and one must deal with suitable generalized solutions the correct class of generalized solutions has only recently been established by the authors this article establishes the convergence of a class of difference approximations to these solutions by obtaining explicit error estimates analogous results are proved by similar means for the method of vanishing viscosity author

asymptotics for the principal eigenvalue and eigenfunction of a nearly first order operator with large potential the asymptotic behaviors of the principal eigenvalue and the corresponding normalized eigenfunction of the operator g e f e 2 f g f l e f for small e are studied under some conditions the first order expansions for them are obtained two applications to risk sensitive control problems are also mentioned

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

identification of almost invariant aggregates in reversible nearly uncoupled markov chains the topic of the present paper has been motivated by a recent computational approach to identify metastable chemical conformations and patterns of conformational changes within molecular systems after proper discretization such conformations show up as almost invariant aggregates in reversible nearly uncoupled markov chains numcs most of the former work on this subject treated the direct problem given the aggregates analyze the loose coupling in connection with the computation of the stationary distribution aggregation disaggregation techniques in contrast to that the present paper focuses on the inverse problem given the system as a whole identify the almost invariant aggregates together with the small probabilities of transitions between them a robust algorithm is worked out on the basis of some detailed perturbation analysis and illustrated at a simple molecular system

on the rate of convergence of the binomial tree scheme for american options an american put option can be modelled as a variational inequality with a penalization approximation to this variational inequality the convergence rate o big delta x 2 3 big of the binomial tree scheme is obtained in this paper

a semi lagrangian approach for natural gas storage valuation and optimal operation the valuation of a gas storage facility is characterized as a stochastic control problem resulting in a hamilton jacobi bellman hjb equation in this paper we present a semi lagrangian method for solving the hjb equation for a typical gas storage valuation problem the method is able to handle a wide class of spot price models that exhibit mean reverting seasonality dynamics and price jumps we develop fully implicit and crank nicolson timestepping schemes based on a semi lagrangian approach and prove the convergence of fully implicit timestepping to the viscosity solution of a modified hjb equation posed on a bounded domain provided that a strong comparison result holds the semi lagrangian approach avoids policy type iterations required by an implicit finite difference method without requiring additional cost numerical experiments are presented for several variants of the basic scheme

dynamic pricing and periodic ordering for a stochastic inventory system with deteriorating items abstract in this paper we consider a problem of the dynamic pricing and the periodic ordering for deteriorating items with a stochastic inventory level depending on the stock dependent demand and the selling price in the model to be established both shortages and remains are allowed and the backlogging rate is variable and dependent on the waiting time for the next replenishment combined with the dynamic pricing a stochastic dynamic optimization model which maximizes the total profit is developed based on the dynamic programming principle the stochastic control model is transformed into a hamilton jacobi bellman hjb equation we show that there exists an optimal replenishment cycle length with an optimal inventory level at start of cycle moreover the optimal pricing strategies are given in addition the finite difference scheme with the semi smooth newton method is proposed to solve the hjb equation numerically and some numerical simulations are presented to illustrate the theoretical results the sensitivity analysis of the optimal solution with respect to the major parameters is carried out and some managerial insights are proposed

entropy solutions in l for the euler equations in nonlinear elastodynamics and related equations a compactness framework is established for approximate solutions to the euler equations in one dimensional nonlinear elastodynamics by identifying new properties of the lax entropies especially the higher order terms in the lax entropy expansions and by developing ways to employ these new properties in the method of compensated compactness then this framework is applied to establish the existence compactness and decay of entropy solutions in l for the euler equations in nonlinear elastodynamics with a more general stress strain relation than those for the previous existence results this compactness framework is further applied to solving the euler equations of conservation laws of mass momentum and energy for a class of thermoelastic media and the equations of motion of viscoelastic media with memory

risk sensitive control on an infinite time horizon stochastic control problems on an infinite time horizon with exponential cost criteria are considered the donsker varadhan large deviation rate is used as a criterion to be optimized the optimum rate is characterized as the value of an associated stochastic differential game with an ergodic expected average cost per unit time cost criterion if we take a small noise limit a deterministic differential game with average cost per unit time cost criterion is obtained this differential game is related to robust control of nonlinear systems

global entropy solutions to weakly nonlinear gas dynamics abstract entropy weak solutions with bounded periodic initial data are considered for the system of weakly nonlinear gas dynamics through a modified glimm scheme an approximate solution sequence is constructed and then a priori estimates are provided with the methods of approximate characteristics and approximate conservation laws which gives not only the existence and uniqueness but also the uniform total variation bounds for the entropy solutions

metastability and low lying spectra in reversible markov chains we study a large class of reversible markov chains with discrete state space and transition matrix pn we define the notion of a set of metastable points as a subset of the state space n such that i this set is reached from any point x n without return to x with probability at least bn while ii for any two points x y in the metastable set the probability t 1x y to reach y from x without return to x is smaller than an 1 bn under some additional non degeneracy assumption we show that in such a situation

singularly perturbed markov decision processes a multiresolution algorithm singular perturbation techniques allow the derivation of an aggregate model whose solution is asymptotically optimal for markov decision processes with strong and weak interactions we develop an algorithm that takes advantage of the asymptotic optimality of the aggregate model in order to compute the solution of the original model we derive conditions for which the proposed algorithm has better worst case complexity than conventional contraction algorithms based on our complexity analysis we show that the major benefit of aggregation is that the reduced order model is no longer ill conditioned the reduction in the number of states due to aggregation is a secondary benefit this is a surprising result since intuition would suggest that the reduced order model can be solved more efficiently because it has fewer states however we show that this is not necessarily the case our theoretical analysis and numerical experiments show that the proposed algorithm can compute the optimal solution with a redu

consistency of generalized finite difference schemes for the stochastic hjb equation we analyze a class of numerical schemes for solving the hjb equation for stochastic control problems which enters the framework of markov chain approximations and generalizes the usual finite difference method the latter is known to be monotonic and hence valid only if the scaled covariance matrix is dominant diagonal we generalize this result by given the set of neighboring points allowed to enter the scheme showing how to compute effectively the class of covariance matrices that is consistent with this set of points we perform this computation for several cases in dimensions 2 3 and 4

linear score tests for variance components in linear mixed models and applications to genetic association studies summary following the rapid development of genome scale genotyping technologies genetic association mapping has become a popular tool to detect genomic regions responsible for certain disease phenotypes especially in early phase pharmacogenomic studies with limited sample size in response to such applications a good association test needs to be 1 applicable to a wide range of possible genetic models including but not limited to the presence of gene by environment or gene by gene interactions and non linearity of a group of marker effects 2 accurate in small samples fast to compute on the genomic scale and amenable to large scale multiple testing corrections and 3 reasonably powerful to locate causal genomic regions the kernel machine method represented in linear mixed models provides a viable solution by transforming the problem into testing the nullity of variance components in this study we consider score based tests by choosing a statistic linear in the score function when the model under the null hypothesis has only one error variance parameter our test is exact in finite samples when the null model has more than one variance parameter we develop a new moment based approximation that performs well in simulations through simulations and analysis of real data we demonstrate that the new test possesses most of the aforementioned characteristics especially when compared to existing quadratic score tests or restricted likelihood ratio tests

on the rate of convergence of finite difference approximations for bellmans equations with variable coefficients the estimates presented here for parabolic bellman s equations with variable coefficients extend the ones earlier obtained for constant coefficients

one and two sided tolerance intervals for general balanced mixed models and unbalanced one way random models in this article we develop procedures for one and two sided tolerance intervals for normal general linear models in which there exists a set of independent scaled chi squared random variables the proposed procedures are based on the concept of generalized pivotal quantities and are applicable to general mixed models provided that balanced data are available however this study focuses on situations involving unbalanced data specific attention is given to the unbalanced one way random model it is shown that the use of generalized pivotal quantities allows the construction of the tolerance intervals of interest fairly straightforward some practical examples are given to illustrate the proposed procedures furthermore detailed statistical simulation studies are conducted to evaluate their performance showing that the proposed procedures can be recommended for practical use

maximal use of central differencing for hamilton jacobi bellman pdes in finance in order to ensure convergence to the viscosity solution the standard method for discretizing hamilton jacobi bellman partial differential equations uses forward backward differencing for the drift term in this paper we devise a monotone method which uses central weighting as much as possible in order to solve the discretized algebraic equations we have to maximize a possibly discontinuous objective function at each node nevertheless convergence of the overall iteration can be guaranteed numerical experiments on two examples from the finance literature show higher rates of convergence for this approach compared to the use of forward backward differencing only

the peierls nabarro model as a limit of a frenkel kontorova model abstract we study a generalization of the fully overdamped frenkel kontorova model in dimension n 1 this model describes the evolution of the position of each atom in a crystal and is mathematically given by an infinite system of coupled first order odes we prove that for a suitable rescaling of this model the solution converges to the solution of a peierls nabarro model which is a coupled system of two pdes typically an elliptic pde in a domain with an evolution pde on the boundary of the domain this passage from the discrete model to a continuous model is done in the framework of viscosity solutions

applications of the cross entropy method to importance sampling and optimal control of diffusions we study the cross entropy method for diffusions one of the results is a versatile cross entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems the approach is based on the minimization of a suitable cross entropy functional with a parametric family of exponentially tilted probability distributions we illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method

delta method and bootstrap in linear mixed models to estimate a proportion when no event is observed application to intralesional resection in bone tumor surgery resecting bone tumors requires good cutting accuracy to reduce the occurrence of local recurrence this issue is considerably reduced with a navigated technology the estimation of extreme proportions is challenging especially with small or moderate sample sizes when no success is observed the commonly used binomial proportion confidence interval is not suitable while the rule of three provides a simple solution unfortunately these approaches are unable to differentiate between different unobserved events different delta methods and bootstrap procedures are compared in univariate and linear mixed models with simulations and real data by assuming the normality the delta method on the z score and parametric bootstrap provide similar results but the delta method requires the estimation of the covariance matrix of the estimates in mixed models the observed fisher information matrix with unbounded variance components should be preferred the parametric bootstrap easier to apply outperforms the delta method for larger sample sizes but it may be time costly copyright 2016 john wiley sons ltd

continuous dependence results for non linear neumann type boundary value problems abstract we obtain estimates on the continuous dependence on the coefficient for second order non linear degenerate neumann type boundary value problems our results extend previous work of cockburn et al jakobsen and karlsen and gripenberg to problems with more general boundary conditions and domains a new feature here is that we account for the dependence on the boundary conditions as one application of our continuous dependence results we derive for the first time the rate of convergence for the vanishing viscosity method for such problems we also derive new explicit continuous dependence on the coefficients results for problems involving bellman isaacs equations and certain quasilinear equation

decay of almost periodic solutions of conservation laws we consider the asymptotic behavior of solutions of systems of inviscid or viscous conservation laws in one or several space variables which are almost periodic in the space variables in a generalized sense introduced by stepanoff and wiener which extends the original one of h bohr we prove that if u x t is such a solution whose inclusion intervals at time t with respect to 0 satisfy l epsiv t t 0 as t and such that the scaling sequence u t x t u t x t t is pre compact as t in l loc 1 d 1 then u x t decays to its mean value which is independent of t as t the decay considered here is in l 1 loc of the variable x t which implies as we show that as t where m x denotes taking the mean value with respect to x in many cases we show that if the initial data are almost periodic in the generalized sense then so also are the solutions we also show in these cases how to reduce the condition on the growth of the inclusion intervals l t with t as t for fixed 0 to a condition on the growth of l 0 with as 0 which amounts to imposing restrictions only on the initial data we show with a simple example the existence of almost periodic non periodic functions whose inclusion intervals satisfy any prescribed growth condition as 0 the applications given here include inviscid and viscous scalar conservation laws in several space variables some inviscid systems in chromatography and isentropic gas dynamics as well as many viscous 2 2 systems such as those of nonlinear elasticity and eulerian isentropic gas dynamics with artificial viscosity among others in the case of the inviscid scalar equations and chromatography systems the class of initial data for which decay results are proved includes in particular the l generalized limit periodic functions our procedures can be easily adapted to provide similar results for semilinear and kinetic relaxations of systems of conservation laws

large time behavior of entropy solutions of conservation laws abstract we are concerned with the large time behavior of discontinuous entropy solutions for hyperbolic systems of conservation laws we present two analytical approaches and explore their applications to the asymptotic problems for discontinuous entropy solutions these approaches allow the solutions of arbitrarily large oscillation without a priori assumption on the ways from which the solutions come the relation between the large time behavior of entropy solutions and the uniqueness of riemann solutions leads to an extensive study of the uniqueness problem we use a direct method to show the large time behavior of large l solutions for a class of m m systems including a model in multicomponent chromatography we employ the uniqueness of riemann solutions and the convergence of self similar scaling sequence of solutions to show the asymptotic behavior of large bv solutions for the 3 3 system of euler equations in thermoelasticity these results indicate that the riemann solution is the unique attractor of large discontinuous entropy solutions whose initial data are l l 1 or bv l 1 perturbation of the riemann data for these systems these approaches also work for proving the large time behavior of approximate solutions to hyperbolic conservation laws

optimal control of molecular dynamics using markov state models a numerical scheme for solving high dimensional stochastic control problems on an infinite time horizon that appear relevant in the context of molecular dynamics is outlined the scheme rests on the interpretation of the corresponding hamilton jacobi bellman equation as a nonlinear eigenvalue problem that using a logarithmic transformation can be recast as a linear eigenvalue problem for which the principal eigenvalue and its eigenfunction are sought the latter can be computed efficiently by approximating the underlying stochastic process with a coarse grained markov state model for the dominant metastable sets we illustrate our method with two numerical examples one of which involves the task of maximizing the population of helices in an ensemble of small biomolecules alanine dipeptide and discuss the relation to the large deviation principle of donsker and varadhan

confidence prediction and tolerance in linear mixed models the literature about prediction interval pi and tolerance interval ti in linear mixed models is usually developed for specific designs which is a main limitation to their use this paper proposes to reformulate the two sided pi to be generalizable under a wide variety of designs one random factor nested and crossed designs for multiple random factors and balanced or unbalanced designs this new methodology is based on the hessian matrix namely the inverse of observed fisher information matrix and is built with a cell mean model the degrees of freedom for the total variance are calculated with the generalized satterthwaite method and compared to the kenward roger s degrees of freedom for fixed effects construction of two sided tis are also detailed with one random factor and two nested and two crossed random variables an extensive simulation study is carried out to compare the widths and coverage probabilities of confidence intervals ci pis and tis to their nominal levels it shows excellent coverage whatever the design and the sample size are finally these cis pis and tis are applied to two real data sets one from orthopedic surgery study intralesional resection risk and the other from assay validation study during vaccine development

one sided tolerance limits in balanced and unbalanced one way random models based on generalized confidence intervals we consider the problem of deriving one sided tolerance intervals in the one way random model with balanced as well as unbalanced data under the usual normality assumptions the problems investigated deal with the computation of such intervals for the observable random variable as well as the unobservable random effect in the one way random model the tolerance limits are derived using the concept of a generalized confidence interval some approximations are derived for the tolerance limits and their performance is investigated by simulation the simulation results show that the proposed tolerance limits are quite satisfactory for practical use

microscopic theory of isothermal elastodynamics this paper examines random perturbations of the anharmonic chain of coupled oscillators the microscopic system has two conservation laws and its hyperbolic scaling limit results in the quasi linear wave equation p system of isothermal isentropic elasticity in the shock regime the compensated compactness method is used lastly results from j w shearer and d serre are applied

long time existence of entropy solutions to the one dimensional non isentropic euler equations with periodic initial data the non isentropic euler system with periodic initial data in mathbb r 1 is studied by analyzing wave interactions in a framework of specially chosen riemann invariants generalizing glimm s functionals and applying the method of approximate conservation laws and approximate characteristics an mathcal o varepsilon 2 lower bound is established for the life span of the entropy solutions with initial data that possess varepsilon variation in each period

one sided and two sided tolerance intervals in general mixed and random effects models using small sample asymptotics the computation of tolerance intervals in mixed and random effects models has not been satisfactorily addressed in a general setting when the data are unbalanced and or when covariates are present this article derives satisfactory one sided and two sided tolerance intervals in such a general scenario by applying small sample asymptotic procedures in the case of one sided tolerance limits the problem reduces to the interval estimation of a percentile and accurate confidence limits are derived using small sample asymptotics in the case of a two sided tolerance interval the problem does not reduce to an interval estimation problem however it is possible to derive an approximate margin of error statistic that is an upper confidence limit for a linear combination of the variance components for the latter problem small sample asymptotic procedures can once again be used to arrive at an accurate upper confidence limit in the article balanced and unbalanced data situations are treated separately and

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

decay of entropy solutions of nonlinear conservation laws we are concerned with the asymptotic behavior of entropy solutions of nonlinear conservation laws the main objective of this paper is to present an analytical approach and to explore its applications to studying the large time behavior of periodic entropy solutions of hyperbolic conservation laws the asymptotic decay of periodic solutions of nonlinear hyperbolic conservation laws is an important nonlinear phenomenon it is observed that the genuine nonlinearity of equations forces the waves of each characteristic family to interact vigorously and to cancel each other the insightful analysis of glimm lax gl for scalar equations and 2 2 systems has indicated that the resultant mutual cancellation of interacting shock and rarefaction waves of the same family induces the decay of periodic solutions such a result was first shown by lax l1 in 1957 for one dimensional convex scalar conservation laws dafermos d1 applying his uniform processes proved the decay result for the case that the set of inflection points of the flux does not have an accumulation point the glimm lax theory gl indicates that for 2 2 strictly hyperbolic and genuinely nonlinear systems any periodic glimm solution decays like o 1 t this result was proved by using the approximate characteristic method in the glimm difference solutions provided that the oscillation of the corresponding initial data is small recently using the method of generalized characteristics dafermos d3 showed that any periodic solution with local bounded variation and small oscillation for 2 2 systems decays asymptotically with the same detailed structure pas found by lax l1 for the

error bounds for monotone approximation schemes for hamilton jacobi bellman equations we obtain error bounds for monotone approximation schemes of hamilton jacobi bellman equations these bounds improve previous results of krylov and the authors the key step in the proof of these new estimates is the introduction of a switching system which allows the construction of approximate almost smooth supersolutions for the hamilton jacobi bellman equation

continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations using the maximum principle for semicontinuous functions 3 4 we prove a general continuous dependence on the nonlinearities estimate for bounded holder continuous viscosity solutions of fully nonlinear degenerate elliptic equations furthermore we provide existence uniqueness and holder continuity results for bounded viscosity solutions of such equations our results are general enough to encompass hamilton jacobi bellman isaacs s equations of zero sum two player stochastic dierential games an immediate conse quence of the results obtained herein is a rate of convergence for the vanishing viscosity method for fully nonlinear degenerate elliptic equations

probabilistic error analysis for some approximation schemes to optimal control problems abstract we introduce a class of numerical schemes for optimal stochastic control problems based on a novel markov chain approximation which uses in turn a piecewise constant policy approximation euler maruyama time stepping and a gaus hermite approximation of the gausian increments we provide lower error bounds of order arbitrarily close to 1 2 in time and 1 3 in space for lipschitz viscosity solutions coupling probabilistic arguments with regularization techniques as introduced by krylov the corresponding order of the upper bounds is 1 4 in time and 1 5 in space for sufficiently regular solutions the order is 1 in both time and space for both bounds finally we propose techniques for further improving the accuracy of the individual components of the approximation

risk sensitivity large deviations and stochastic control abstract an exponential function of cost is adopted as a risk sensitive criterion and reasons given that this choice should be a natural one it is shown that the analysis leads to risk sensitive versions of the certainty equivalence principle separation principle and of the maximum principle and that these have a validity even outside the usual linear quadratic gaussian framework the methods are applied to some simple examples of economic interest

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

the vanishing viscosity method in one dimensional thermoelasticity the vanishing viscosity method is applied to the system of conservation laws of mass momentum and energy for a special class of one dimensional thermoelastic media that do not conduct heat two types of vanishing viscosity are considered newtonian and artificial in both cases accompanied by vanishing heat conductivity it is shown that in either case one can pass to the zero viscosity limit by the method of compensated compactness provided that velocity and pressure are uniformly bounded oscillations in the entropy field may propagate along the linearly degenerate characteristic field but do not affect the compactness of the velocity field or the pressure field a priori bounds on velocity and pressure are established albeit only for the case of artificial viscosity