Large deviations of the empirical flow for continuous time Markov chains

We consider a continuous time Markov chain on a countable state space and prove a joint large deviation principle for the empirical measure and the empirical flow, which accounts for the total number of jumps between pairs of states. We give a direct proof using tilting and an indirect one by contra...

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Veröffentlicht in:	Annales de l'I.H.P. Probabilités et statistiques 2015-08, Vol.51 (3), p.867-900
Hauptverfasser:	Bertini, Lorenzo, Faggionato, Alessandra, Gabrielli, Davide
Format:	Artikel
Sprache:	eng
Schlagworte:	60F10 60J27 82C05 Empirical flow Entropy Large deviations principle Markov chain
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creator	Bertini, Lorenzo Faggionato, Alessandra Gabrielli, Davide
description	We consider a continuous time Markov chain on a countable state space and prove a joint large deviation principle for the empirical measure and the empirical flow, which accounts for the total number of jumps between pairs of states. We give a direct proof using tilting and an indirect one by contraction from the empirical process.
doi_str_mv	10.1214/14-AIHP601
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subjects	60F10 60J27 82C05 Empirical flow Entropy Large deviations principle Markov chain
title	Large deviations of the empirical flow for continuous time Markov chains
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