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

Citation
Dupuis, Paul et Liu, Yufei, On the large deviation rate function for the empirical measures of reversible jump Markov processes, Annals of probability , 43(3), 2015, pp. 1121-1156
Journal title
ISSN journal
00911798
Volume
43
Issue
3
Year of publication
2015
Pages
1121 - 1156
Database
ACNP
SICI code
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.