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2006 Relative entropy and waiting times for continuous-time Markov processes
Jean-René Chazottes, Cristian Giardina, Frank Redig
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Electron. J. Probab. 11: 1049-1068 (2006). DOI: 10.1214/EJP.v11-374


For discrete-time stochastic processes, there is a close connection between return (resp. waiting) times and entropy (resp. relative entropy). Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one needs a reference measure on path space and so the natural object is relative entropy rather than entropy. In this paper we elaborate on this in the case of continuous-time Markov processes with finite state space. A reference measure of special interest is the one associated to the time-reversed process. In that case relative entropy is interpreted as the entropy production rate. The main results of this paper are: almost-sure convergence to relative entropy of the logarithm of waiting-times ratios suitably normalized, and their fluctuation properties (central limit theorem and large deviation principle).


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Jean-René Chazottes. Cristian Giardina. Frank Redig. "Relative entropy and waiting times for continuous-time Markov processes." Electron. J. Probab. 11 1049 - 1068, 2006.


Accepted: 28 November 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1127.60071
MathSciNet: MR2268537
Digital Object Identifier: 10.1214/EJP.v11-374

Primary: 60J27
Secondary: 60F10

Keywords: central limittheorem , continuous-time Markov chain , entropy production , large deviations , Law of Large Numbers , time-reversed process


Vol.11 • 2006
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