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Markov process large deviations in [tau]-topology

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  • Bolthausen, Erwin

Abstract

The results of Donsker and Varadhan on the probability of large deviations for empirical measures (or occupation measures) of uniformly ergodic Markov processes are extended. Usually the large deviation results are formulated in the weak topology on the set of probability measures. We extend this to the topology which is generated by the integrals over bounded measurable functions.

Suggested Citation

  • Bolthausen, Erwin, 1987. "Markov process large deviations in [tau]-topology," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 95-108.
    • Handle: RePEc:eee:spapps:v:25:y:1987:i::p:95-108
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    Cited by:

    1. Hu, Yijun, 1995. "A note on the relationship between the rate functions for stationary dependent random sequences in [tau]-topology and the relative entropy," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 351-355, April.
    2. Jingjia Liu & Quirin Vogel, 2021. "Large Deviations of the Range of the Planar Random Walk on the Scale of the Mean," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2315-2345, December.
    3. 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.
    4. Yeor Hafouta & Yuri Kifer, 2016. "A Nonconventional Local Limit Theorem," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1524-1553, December.

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