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September 2016 Large deviations for the empirical measure of heavy-tailed Markov renewal processes
Mauro Mariani, Lorenzo Zambotti
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Adv. in Appl. Probab. 48(3): 648-671 (September 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.

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Mauro Mariani. Lorenzo Zambotti. "Large deviations for the empirical measure of heavy-tailed Markov renewal processes." Adv. in Appl. Probab. 48 (3) 648 - 671, September 2016.

Information

Published: September 2016
First available in Project Euclid: 19 September 2016

zbMATH: 1351.60031
MathSciNet: MR3568885

Subjects:
Primary: 60F10 , 60K15

Keywords: empirical measure , heavy tail , large deviation , Markov renewal process

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 3 • September 2016
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