摘要:

For the multidimensional Dirichlet problem of the Poisson equation on an arbitrary compact domain, this study examines convergence properties with rates of approximate solutions, obtained by a standard difference scheme over inscribed uniform grids. Sharp quantitative estimates are given by the use of second moduli of continuity of the second single partial derivatives of the exact solution. This is achieved by employing the probabilistic method of simple random walk

ISSN:0736-2994    

DOI:10.1080/07362999808809542

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In a previous paper we introduced a general class of shapepreserving wavelet approximating operators (approximators) which transform cumulative distribution functions (cdf) and densities into functions of the same type. Empirical versions of these operators are used in this paper to introduce, in an unified way, shape- preserving wavelet estimators of cdf and densities, with a priori prescribed smoothness properties. We evaluate their risk for a variety of loss functions and analyze their asymptotic behavior. We study the convergence rates depending on minimal additional assumptions about the cdf/ density. These assumptions are in terms of the function belonging to certain homogeneous Besov or Triebel- Lizorkin spaces and others. As a main evaluation tool the integral p-modulus of smoothness is used

ISSN:0736-2994    

DOI:10.1080/07362999808809543

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

This paper gives extensions of the Doob and Burkholder inequalities for certain classes of random fields. The Brennan-Doob inequality for V-quasimartingales is extended to the case p > 1 and is shown to hold for the class of decomposable processes satisfying the Doob inequality of Wong and Zakai [10]. A Doob inequality for the class ofi-martingales having finite quadratic variation in the non-martingale coordinate is shown. For the class of quasi martingales having independent increments two Burkholder-type inequalities are derived

ISSN:0736-2994    

DOI:10.1080/07362999808809544

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In this paper exact constants are given for the rate of convergence of the solutionxnof the nonlinear difference equationtowards the root θ offunder very general conditions on the steplengthsan, on the weighting factorsbnand on the random noisevn. Moreover, an almost sure representation is developed for the deviationxn– θ by weighted sums of (independent) random variables

ISSN:0736-2994    

DOI:10.1080/07362999808809545

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

We define a set-valued stochastic process and an integral of a such process with respect to a semimartingale. Next we consider a stochastic integral inclusion. Using fixed point methods we prove some results on the existence of its solutions

ISSN:0736-2994    

DOI:10.1080/07362999808809546

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

This paper deals with notions which allow us to compare the degree of developments of dynamic systems. The classical definition of stability can be obtained by comparing the considered system with the trivial equation Ẋ ¦ 0. In the linear cases, this definition leads to the comparison of the top essup - exponents of these systems. We are also concerned with the control problem of Lyapunov exponents for choosing “a stablest system”. The existence of optimal controls is proved

ISSN:0736-2994    

DOI:10.1080/07362999808809547

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

The rate of convergence for an almost surely convergent seriesof random variables {Xn, n≥ 1} is studied in this paper. More specifically, ifSnconverges almost surely to a random variableSthen the tail seriesis a well-defined sequence of random variable withTn→ 0 almost surely. The main result provides conditions for each ofto hold for given numerical sequences. As special cases, new results are obtained when {Xn, n≥ 1} is a martingale difference sequence and when theXn's are of the form, where {an, n≥ 1} is a sequence of constants and {Yn, n≥ 1} is an orthogonal system of exchangeable random variables. An application to the Polya urn scheme is considered. The current work generalizes and simplifies some of the recent results of Nam and Rosalsky [15]

ISSN:0736-2994    

DOI:10.1080/07362999808809548

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In this paper, we discuss a (Co)-group generated by the Lévy Laplacian acting on a domain in the space of Hida distributions. We also give a relationship between the analytic extension of this (Co)-group and the adjoint operator of an infinite dimensional Fourier-Mehler transform introduced by H.- H. Kuo

ISSN:0736-2994    

DOI:10.1080/07362999808809549

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

This paper considers an infinite server queue in continuous time in which arrivals are in batches of variable size X and service is provided in groups of fixed size R. We obtain analytical results for the number of busy servers and waiting customers at arbitrary time points. For the number of busy servers, we obtain a recursive relation for the partial binomial moments both in transient and steady states. Special cases are also discussed

ISSN:0736-2994    

DOI:10.1080/07362999808809550

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

ISSN:0736-2994    

DOI:10.1080/07362999808809541

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor