## The Annals of Probability

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 60F10: Large deviations

Secondary: 60J05: Discrete-time Markov processes on general state spaces

**Keywords**

Average occupation time large deviations Markov process indecomposability symmetric random walks Harris' chains

#### Citation

Chiang, Tzuu-Shuh. A Lower Bound of the Asymptotic Behavior of Some Markov Processes. Ann. Probab. 10 (1982), no. 4, 955--967. doi:10.1214/aop/1176993717. https://projecteuclid.org/euclid.aop/1176993717