Gaussian limit theorems for diffusion processes and an application

Joseph G. Conlon, Renming Song

Research output: Contribution to journalArticlepeer-review

Abstract

Suppose that L=∑i,j=1daij(x)∂ 2/∂xi∂xj is uniformly elliptic. We use XL(t) to denote the diffusion associated with L. In this paper we show that, if the dimension of the set {x:[aij(x)]≠12I} is strictly less than d, the random variable (XL(T)-XL(0))/T converges in distribution to a standard Gaussian random variable. In 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.

Original languageEnglish (US)
Pages (from-to)103-128
Number of pages26
JournalStochastic Processes and their Applications
Volume81
Issue number1
DOIs
StatePublished - May 1 1999

Keywords

  • Diffusions
  • Random environments
  • Random walks

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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