Large deviations for the empirical measure of Markov renewal processes

Details Large deviations for the empirical measure of Markov renewal processes Large deviations for the empirical measure of Markov renewal processes

2012-03-27

arxiv.org/abs/1203.5930v1

Mathematics

Probability

Scientific paper

A large deviations principle is established for the joint law of the empirical measure and the flow measure of a renewal Markov process on a finite graph. We do not assume any bound on the arrival times, allowing heavy tailed distributions. In particular, the rate functional is in general degenerate (it has a nontrivial set of zeros) and not strictly convex. These features show a behavior highly different from what one may guess with a heuristic Donsker-Varadhan analysis of the problem.

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