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May 2015 On the large deviation rate function for the empirical measures of reversible jump Markov processes
Paul Dupuis, Yufei Liu
Ann. Probab. 43(3): 1121-1156 (May 2015). DOI: 10.1214/13-AOP883

Abstract

The large deviations principle for the empirical measure for both continuous and discrete time Markov processes is well known. Various expressions are available for the rate function, but these expressions are usually as the solution to a variational problem, and in this sense not explicit. An interesting class of continuous time, reversible processes was identified in the original work of Donsker and Varadhan for which an explicit expression is possible. While this class includes many (reversible) processes of interest, it excludes the case of continuous time pure jump processes, such as a reversible finite state Markov chain. In this paper, we study the large deviations principle for the empirical measure of pure jump Markov processes and provide an explicit formula of the rate function under reversibility.

Citation

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Paul Dupuis. Yufei Liu. "On the large deviation rate function for the empirical measures of reversible jump Markov processes." Ann. Probab. 43 (3) 1121 - 1156, May 2015. https://doi.org/10.1214/13-AOP883

Information

Published: May 2015
First available in Project Euclid: 5 May 2015

zbMATH: 1325.60023
MathSciNet: MR3342660
Digital Object Identifier: 10.1214/13-AOP883

Subjects:
Primary: 60E10, 60J75

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 3 • May 2015
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