摘要:

In continuous time, rates of convergence of density estimators fluctuate with the nature of observed sample paths. In this paper, we give a family of rates reached by the kernel estimator and we show that these rates are minimax. Finally, we study applications of these results for specific classes of processes including the Gaussian ones

ISSN:0736-2994    

DOI:10.1080/07362990008809702

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

Many decision problems can be characterized by a set of possible states and a cost associated with each possible state transition, hi this paper we discuss how to select a policy from a set of possible policies in the long term. If the cost matrix is not available the transition matrix can be used to compare expected return times to states. In our setting the transition matrix is defined by use of linguistic terms and as a consequence, the expected return times are fuzzy. In the case where the cost matrix is available, fuzzy average costs are computed. The resulting fuzzy quantities are compared by introducing the concept of minimizing sets. Finally, we look at the case where the transition takes place from a state to a state that is known to be an element of some subset of states, but we do not know which one. We use the Dempster–Shafer theory [Shafer 1976] together with techniques of Norton [Norton 1988] and Smetz [Smetz 1976] to approximate the transition probabilities

ISSN:0736-2994    

DOI:10.1080/07362990008809703

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

This paper studies stochastic particle systems related to the coagulation fragmentation equation. For a certain class of unbounded coagulation kernels and fragmentation rates, relative compactness of the stochastic systems is established and weak accumulation points are characterized as solutions. These results imply a new existence theorem. Finally a simulation algorithm based on the particle systems is proposed

ISSN:0736-2994    

DOI:10.1080/07362990008809704

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

In this paper, three classes of preconditioners are proposed for solving some stochastic integral equations with the weakly singular kernel and the hypersingular kernel. The first and the second class of preconditioners are based on circulant operators, but the third class of preconditioners is based on iterative substructuring. It is proved that substructuring preconditioners can be better than other preconditioners. Also, the spaces of solutions are discussed such that the solutions of these equations are smooth, therefore, we give special Banach spaces for these integral equations. Finally, numerical results which support our theories are presented

ISSN:0736-2994    

DOI:10.1080/07362990008809705

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

The paper deals with a class of random variational inequalities and simple random elliptic boundary value problems with unilateral conditions. Here randomness enters in the coefficient of the elliptic operator and in the right hand side of the p.d.e. In addition to existence and uniqueness results a theory of combined probabilistic deterministic discretization is developped that includes nonconforming approxima¬tion of unilateral constraints. Without any regularity assumptions on the solution, norm convergence of the full approximation process is established. The theory is applied to a Helmholtz like elliptic equation with Signorini boundary conditions as a simple model problem, where Galerkin discretization is realized by finite element approximation

ISSN:0736-2994    

DOI:10.1080/07362990008809706

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

In this paper, we establish the Lyapunov function characterization which is a sufficient and necessary condition for mild solutions of semilinear stochastic evolution equations to be exponentially stable in mean square. We also study the Lyapunov function characterization of ultimate exponential boundedness, a concept which is closely related to the existence of invariant measures of non-stationary stochastic evolution equations

ISSN:0736-2994    

DOI:10.1080/07362990008809707

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

In this paper we shall investigate the stability of a stochastic integro–differential equationwhich is regarded as a stochastically perturbed system of a given non-linear stable system. Several sufficient criteria are obtained under which the systemcan tolerate the stochastic perturbation without losing the property of stability

ISSN:0736-2994    

DOI:10.1080/07362990008809708

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

Let {Wtt⩾ 0} be a one-dimensional Brownian motion starting from. Strassen's functional iterated logarithm law implies that almost surely limThis paper gives a functiong(t) such that limsupis almost surely a finite positive constant, which improves a previous result of Chan [2]. The lower limits ofX(t) are also studied

ISSN:0736-2994    

DOI:10.1080/07362990008809709

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

The existence of a solution of a large class of nonlinear stochastic inclusions is shown. The existence of an open loop problem for those stochastic inclusions, is established. Application to an optimal strategy problem arising in the fight against drugs is given.

ISSN:0736-2994    

DOI:10.1080/07362990008809710

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

The purpose of this work is to obtain sufficient conditions for transience and recurrence of multidimensional jump–diffusion processes, which are driven by Brownian motion and Poisson random measure. The approach adopted here is to construct appropriate Lyapounov functions

ISSN:0736-2994    

DOI:10.1080/07362990008809711

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor