Advances in Applied Probability

Large deviations for the empirical measure of heavy-tailed Markov renewal processes

Mauro Mariani and Lorenzo Zambotti

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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.

Article information

Source
Adv. in Appl. Probab., Volume 48, Number 3 (2016), 648-671.

Dates
First available in Project Euclid: 19 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.aap/1474296308

Mathematical Reviews number (MathSciNet)
MR3568885

Zentralblatt MATH identifier
1351.60031

Subjects
Primary: 60F10: Large deviations 60K15: Markov renewal processes, semi-Markov processes

Keywords
Large deviation empirical measure Markov renewal process heavy tail

Citation

Mariani, Mauro; Zambotti, Lorenzo. Large deviations for the empirical measure of heavy-tailed Markov renewal processes. Adv. in Appl. Probab. 48 (2016), no. 3, 648--671. https://projecteuclid.org/euclid.aap/1474296308


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