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Relative entropy and waiting times for continuous-time Markov processes

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1.	Title	Title of document	Relative entropy and waiting times for continuous-time Markov processes
2.	Creator	Author's name, affiliation, country	Jean-René Chazottes; CPht, CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, France.
2.	Creator	Author's name, affiliation, country	Cristian Giardina; Eurandom, Postbus 513, 5600 MB Eindhoven, the Netherlands
2.	Creator	Author's name, affiliation, country	Frank Redig; Mathematical Institute Leiden university
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	continuous-time Markov chain, law of large numbers, central limittheorem, large deviations, entropy production, time-reversed process
3.	Subject	Subject classification	60J27;60F10
4.	Description	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).
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Cristian Giardina thanks NWO project 613000435 (exponential laws for rare events in spatiallyextended random systems) for finanicial support
7.	Date	(YYYY-MM-DD)	2006-11-28
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/374
10.	Identifier	Digital Object Identifier	10.1214/EJP.v11-374
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 11
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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