Electronic Journal of Probability

Relative entropy and waiting times for continuous-time Markov processes

Jean-René Chazottes, Cristian Giardina, and Frank Redig

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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).

Article information

Source
Electron. J. Probab., Volume 11 (2006), paper no. 40, 1049-1068.

Dates
Accepted: 28 November 2006
First available in Project Euclid: 31 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464730575

Digital Object Identifier
doi:10.1214/EJP.v11-374

Mathematical Reviews number (MathSciNet)
MR2268537

Zentralblatt MATH identifier
1127.60071

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60F10: Large deviations

Keywords
continuous-time Markov chain law of large numbers central limittheorem large deviations entropy production time-reversed process

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Chazottes, Jean-René; Giardina, Cristian; Redig, Frank. Relative entropy and waiting times for continuous-time Markov processes. Electron. J. Probab. 11 (2006), paper no. 40, 1049--1068. doi:10.1214/EJP.v11-374. https://projecteuclid.org/euclid.ejp/1464730575


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