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• W265594243 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)." @default.
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• W265594243 date "2006-01-01" @default.
• W265594243 modified "2023-09-25" @default.
• W265594243 title "Relative entropy and waiting times for continuous-time Markov processes" @default.
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• W265594243 doi "https://doi.org/10.1214/ejp.v11-374" @default.
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