On the Large Deviation Rate Function for the Empirical Measures of Reversible Jump Markov Processes
BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS
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The large deviations principle for the empirical measure for both continuous and discrete time Markov processes is well known. Various expressions are avail- able 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 con- tinuous time, reversible processes was identi ed in the original work of Donsker and Varadhan for which an explicit expression is possible. While this class in- cludes many reversible processes of interest, it excludes the case of continuous time pure jump processes, such as a reversible nite 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.
- Statistics and Probability