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November, 1982 A Lower Bound of the Asymptotic Behavior of Some Markov Processes
Tzuu-Shuh Chiang
Ann. Probab. 10(4): 955-967 (November, 1982). DOI: 10.1214/aop/1176993717

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.

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Tzuu-Shuh Chiang. "A Lower Bound of the Asymptotic Behavior of Some Markov Processes." Ann. Probab. 10 (4) 955 - 967, November, 1982. https://doi.org/10.1214/aop/1176993717

Information

Published: November, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0499.60030
MathSciNet: MR672296
Digital Object Identifier: 10.1214/aop/1176993717

Subjects:
Primary: 60F10
Secondary: 60J05

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

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 4 • November, 1982
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