A large deviations principle is established for the joint law of the empirical measure and the flow measure of a Markov renewal process on a finite graph. We do not assume any bound on the arrival times, allowing heavy-tailed distributions. In particular, the rate function is in general degenerate (it has a nontrivial set of zeros) and not strictly convex. These features show a behaviour highly different from what one may guess with a heuristic Donsker-Varadhan analysis of the problem.
Large deviations for the empirical measure of heavy-tailed markov renewal processes / Mariani, Mauro; Zambotti, Lorenzo. - In: ADVANCES IN APPLIED PROBABILITY. - ISSN 0001-8678. - STAMPA. - 48:3(2016), pp. 648-671. [10.1017/apr.2016.21]
Large deviations for the empirical measure of heavy-tailed markov renewal processes
MARIANI, Mauro;
2016
Abstract
A large deviations principle is established for the joint law of the empirical measure and the flow measure of a Markov renewal process on a finite graph. We do not assume any bound on the arrival times, allowing heavy-tailed distributions. In particular, the rate function is in general degenerate (it has a nontrivial set of zeros) and not strictly convex. These features show a behaviour highly different from what one may guess with a heuristic Donsker-Varadhan analysis of the problem.| File | Dimensione | Formato | |
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