Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Large deviations of the empirical flow for continuous time Markov chains

Lorenzo Bertini, Alessandra Faggionato, and Davide Gabrielli

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Abstract

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.

Résumé

On considère une chaîne de Markov en temps continu à espace d’états denombrable, et on prouve un principe de grandes déviations commun pour la mesure empirique et le courant empirique, qui représente le nombre total de sauts entre les paires d’états. On donne une preuve directe à l’aide d’un tilting, et une preuve indirecte par contraction, à partir du processus empirique.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 51, Number 3 (2015), 867-900.

Dates
Received: 1 May 2013
Revised: 6 January 2014
Accepted: 20 January 2014
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1435759232

Digital Object Identifier
doi:10.1214/14-AIHP601

Mathematical Reviews number (MathSciNet)
MR3365965

Zentralblatt MATH identifier
1323.60045

Subjects
Primary: 60F10: Large deviations 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 82C05: Classical dynamic and nonequilibrium statistical mechanics (general)

Keywords
Markov chain Large deviations principle Entropy Empirical flow

Citation

Bertini, Lorenzo; Faggionato, Alessandra; Gabrielli, Davide. Large deviations of the empirical flow for continuous time Markov chains. Ann. Inst. H. Poincaré Probab. Statist. 51 (2015), no. 3, 867--900. doi:10.1214/14-AIHP601. https://projecteuclid.org/euclid.aihp/1435759232


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