## The Annals of Probability

### A Lower Bound of the Asymptotic Behavior of Some Markov Processes

Tzuu-Shuh Chiang

#### Abstract

Let $X_0, X_1 \cdots$ be a Markov process with transition function $p(x, dy)$. Let $L_n(\omega, \cdot)$ be its average occupation time measure, i.e., $L_n(\omega, A)= 1/n \cdot \sum^{n-1}_{i=0} \chi A(x_i(\omega))$. A powerful theorem concerning the lower bound of the asymptotic behavior of $L_n(\omega, \cdot)$ was proved by Donsker and Varadhan when $p(x, dy)$ satisfies a homogeneity condition. This paper tries to extend their results to some cases where such a homogeneity condition is not satisfied. This particularly includes symmetric random walks and Harris' chains.

#### Article information

Source
Ann. Probab., Volume 10, Number 4 (1982), 955-967.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993717

Digital Object Identifier
doi:10.1214/aop/1176993717

Mathematical Reviews number (MathSciNet)
MR672296

Zentralblatt MATH identifier
0499.60030

JSTOR