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arXiv · math/0512386

Relative entropy and waiting times for continuous-time Markov processes

Jean-Rene Chazottes·Cristian Giardina·Frank Redig
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Abstract

For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one does need a reference measure 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 suitable waiting-times and their fluctuation properties (central limit theorem and large deviation principle).

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Jean-Rene Chazottes, Cristian Giardina, Frank Redig. 2005-12-16. Relative entropy and waiting times for continuous-time Markov processes. https://arxiv.org/abs/math/0512386

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