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

Zambotti, Lorenzo; Mariani, Mauro, Large deviations for the empirical measure of heavy tailed Markov renewal processes, Advances in Applied Probability;0001-8678, 48, 3, p. 648-671. 10.1017/apr.2016.21

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/pdf/1203.5930.pdf
Journal name
Advances in Applied Probability;0001-8678
Volume
48
Number
3
Publisher
Applied Probability Trust
Pages
648-671
Publication identifier
Metadata
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Author(s)
Zambotti, Lorenzo cc
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Mariani, Mauro
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
heavy tail; Markov renewal process; empirical measure; Large deviation