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Relative entropy and waiting times for continuous-time Markov processes

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2006-11-28
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Chazottes, J. R.
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Relative entropy and waiting times for continuous-time Markov processes
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  • Chazottes, J. R.;
  • Giardina, C.;
  • Redig, F.;
Abstract
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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URI: https://repositorio.uchile.cl/handle/2250/124792
ISSN: 1083-6489
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ELECTRONIC JOURNAL OF PROBABILITY Volume: 11 Pages: 1049-1068 Published: NOV 28 2006
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