摘要:

Let (E)βandbe the space of test and generalized white noise functionals, respectively. It is proved that for each positive integerkwe construct explicitly one-parameter semigroup and cosine family of operators on an appropriate (E)βspace of which infinitesimal generator is. As an application, we will prove the existence and uniqueness of solutions of the Cauchy problems for the first and second order differential equations associated with the operator. Here △GandNare the Gross Laplacian and the number operator on (E)β, respectively. Also, we investigate the existence and uniqueness of solutions of the Cauchy problems associated with the operatoris the adjoint operator of △G

ISSN:0736-2994    

DOI:10.1080/07362999908809585

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

New explicit stability conditions are derived for stochastic integro-differential equations with operator coefficients. The equations under consideration arise in the analysis of viscoelastic structural members driven by random excitations. Unlike previous studies, the coefficients are not assumed to be self-adjoint and commuting operators. Our stability conditions are formulated in terms of norms of the operator coefficients and some auxiliary operators, as well as four specific characteristics of kernels of the integral operators. The conditions developed are applied to determine the critical intensity of random load applied to a system of two viscoelastic bars linked by a glue layer. The effect of material and geometrical parameters of the system on the critical load is analyzed numerically

ISSN:0736-2994    

DOI:10.1080/07362999908809586

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

A semilinear stochastic equation in a Hilbert space is considered, with nonlinearity of gradient type and constant but possibly degenerate diffusion term. Under suitable assumptions, existence and uniqueness of the solution and some smoothing properties for the associated transition semigroup are proved. In particular, strong Feller property and irreducibility are deduced. The main tools are the Malliavin calculus and the Girsanov Theorem

ISSN:0736-2994    

DOI:10.1080/07362999908809587

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

We investigate the existence of a local time process for a class of discontinuous measure branching processes inR.Formally, the local time process is defined aswhereXsis the measure branching process and δ stands for the Dirac function

ISSN:0736-2994    

DOI:10.1080/07362999908809588

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

The rate of convergence for an almost certainly convergent seriesindependent random elements in a real separable Banach space is studied in this paper. More specifically, whenSnconverges almost certainly to a random elementS, the tail seriesis a well defined sequence of random elements withalmost certainly. The main result establishes for a sequence of positive constantswithbj⩽ Const.bnwheneverthe equivalence between the tail series weak law of large numbersand the limit lawthereby extending a result of Nam and Rosalsky [20] to a Banach space setting while also simplifying the argument used in the earlier result. The quasimonotonicity proviso oncannot be dispensed with

ISSN:0736-2994    

DOI:10.1080/07362999908809589

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

This work discusses the problem of estimating a nonlinear signal process with nonadditive non–Gaussian noise via a marked point process observation. We begin by introducing a modeling of discrete–time marked point processes. In order to derive the exact filter, namely the conditional density of the signal given the observation history, a reference probability is introduced; this probability measure renders the signal and the observation processes independent, as needed. We present a discretetime version of Zakai equation corresponding to our model. By specializing the signal to be linear, we moreover show, under suitable assumptions, that the filter is finite dimensional

ISSN:0736-2994    

DOI:10.1080/07362999908809590

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

We study the link between linear backward-forward stochastic differential equations and the problem of existence of Nash equilibrium points in nonzero sum linear–quadratic stochastic differential games. For such games we show the existence of an equilibrium point whose expression is given

ISSN:0736-2994    

DOI:10.1080/07362999908809591

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0736-2994    

DOI:10.1080/07362999908809584

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor