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

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Link to item file
https://arxiv.org/pdf/1203.5930.pdf
Dewey
Probabilités et mathématiques appliquées
Sujet
heavy tail; Markov renewal process; empirical measure; Large deviation
Journal issue
Advances in Applied Probability;0001-8678
Volume
48
Number
3
Publication date
09-2016
Article pages
648-671
Publisher
Applied Probability Trust
DOI
http://dx.doi.org/10.1017/apr.2016.21
URI
https://basepub.dauphine.fr/handle/123456789/17420
Collections
  • CEREMADE : Publications
Metadata
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Author
Zambotti, Lorenzo
102 Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Mariani, Mauro
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
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.

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