Gaussian limit theorems for diffusion processes and an application

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:81

Article

Conlon, JC ; Song, RM

关键词: random walks;    diffusions;    random environments;   

DOI  :  10.1016/S0304-4149(98)00095-7

来源: Elsevier

【 摘 要 】

Suppose that L = Sigma(i,) (d)(j=1), a(ij)(x)partial derivative(2)/partial derivative x(i)partial derivative x(j) is uniformly elliptic, We use X-L(1) to denote the diffusion associated with L. In this paper we show that, if the dimension of the set {x:[a(ij)(x)] not equal 1/2I} is strictly less than d, the random variable (X-L(T) - X-L(0))/root T converges in distribution to a standard Gaussian random variable. Ln fact, we also provide rates of convergence. As an application, these results are used to study a problem of a random walk in a random environment. (C) 1999 Elsevier Science B.V. All rights reserved.

【 授权许可】

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