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August 2015 Large deviations of the empirical flow for continuous time Markov chains
Lorenzo Bertini, Alessandra Faggionato, Davide Gabrielli
Ann. Inst. H. Poincaré Probab. Statist. 51(3): 867-900 (August 2015). DOI: 10.1214/14-AIHP601

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.

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.

Citation

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Lorenzo Bertini. Alessandra Faggionato. Davide Gabrielli. "Large deviations of the empirical flow for continuous time Markov chains." Ann. Inst. H. Poincaré Probab. Statist. 51 (3) 867 - 900, August 2015. https://doi.org/10.1214/14-AIHP601

Information

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

zbMATH: 1323.60045
MathSciNet: MR3365965
Digital Object Identifier: 10.1214/14-AIHP601

Subjects:
Primary: 60F10, 60J27
Secondary: 82C05

Rights: Copyright © 2015 Institut Henri Poincaré

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Vol.51 • No. 3 • August 2015
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