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Bolthausen, E; Schmock, U (1989). On the maximum entropy principle for uniformly ergodic Markov chains. Stochastic Processes and their Applications, 33(1):1-27.

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For strongly ergodic discrete time Markov chains we discuss the possible limits as n→∞ of probability measures on the path space of the form exp(nH(Ln)) dP/Zn· Ln is the empirical measure (or sojourn measure) of the process, H is a real-valued function (possibly attaining −∞) on the space of probability measures on the state space of the chain, and Zn is the appropriate norming constant. The class of these transformations also includes conditional laws given Ln belongs to some set. The possible limit laws are mixtures of Markov chains minimizing a certain free energy. The method of proof strongly relies on large deviation techniques.


15 citations in Web of Science®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:maximum entropy; large deviations; Markov chains; variational problem; weak convergence
Deposited On:04 Nov 2009 14:31
Last Modified:27 Nov 2013 16:42
Publisher DOI:10.1016/0304-4149(89)90063-X
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1027105

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