Large deviations of the empirical flow for continuous time Markov chains

Bertini, Lorenzo; Faggionato, Alessandra; Gabrielli, Davide

Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 3, pp. 867-900.

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.

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.

Mots clés : Markov chain, large deviations principle, entropy, empirical flow

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