The Annals of Probability

On the large deviation rate function for the empirical measures of reversible jump Markov processes

Paul Dupuis and Yufei Liu

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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.

Article information

Source
Ann. Probab., Volume 43, Number 3 (2015), 1121-1156.

Dates
First available in Project Euclid: 5 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.aop/1430830279

Digital Object Identifier
doi:10.1214/13-AOP883

Mathematical Reviews number (MathSciNet)
MR3342660

Zentralblatt MATH identifier
1325.60023

Subjects
Primary: 60E10: Characteristic functions; other transforms 60J75: Jump processes

Keywords
Large deviation rate function reversible Markov process pure jump process empirical measure weak convergence

Citation

Dupuis, Paul; Liu, Yufei. On the large deviation rate function for the empirical measures of reversible jump Markov processes. Ann. Probab. 43 (2015), no. 3, 1121--1156. doi:10.1214/13-AOP883. https://projecteuclid.org/euclid.aop/1430830279


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References

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