Relative entropy and waiting times for continuous-time Markov processes

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dc.creatorChazottes, Jean-Rene
dc.creatorGiardina, Cristian
dc.creatorRedig, Frank
dc.date2005-12-16
dc.date.accessioned2026-07-07T06:55:24Z
dc.date.available2026-07-07T06:55:24Z
dc.descriptionFor 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).
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0512386
dc.identifierhttp://arxiv.org/abs/math/0512386
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106266
dc.subjectProbability
dc.subjectMathematical Physics
dc.titleRelative entropy and waiting times for continuous-time Markov processes
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