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On the maximum entropy principle for uniformly ergodic Markov chains

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  • Bolthausen, Erwin
  • Schmock, Uwe

Abstract

For strongly ergodic discrete time Markov chains we discuss the possible limits as n-->[infinity] 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 -[infinity]) 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.

Suggested Citation

  • Bolthausen, Erwin & Schmock, Uwe, 1989. "On the maximum entropy principle for uniformly ergodic Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 1-27, October.
    • Handle: RePEc:eee:spapps:v:33:y:1989:i:1:p:1-27
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    Citations

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    Cited by:

    1. Horsthemke, Benedikt & Rüttermann, Markus, 1995. "On the maximum entropy principle for a class of stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 117-132, March.
    2. Eichelsbacher, Peter & Schmock, Uwe, 1998. "Exponential approximations in completely regular topological spaces and extensions of Sanov's theorem," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 233-251, September.
    3. Peter Eichelsbacher, 1997. "Large Deviations for Products of Empirical Probability Measures in the τ-Topology," Journal of Theoretical Probability, Springer, vol. 10(4), pages 903-920, October.
    4. Chen, Jinwen & Deng, Xiaoxue, 2013. "Large deviations and related problems for absorbing Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2398-2418.

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