Relative entropy and waiting time for continuous-time Markov processes

J.R. Chazottes, C. Giardinà, F.H.J. Redig

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    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)
    Original languageEnglish
    Pages (from-to)1049-1068
    JournalElectronic Journal of Probability
    Publication statusPublished - 2006


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