Large deviations for occupation measures of Markov processes: Discrete time, noncompact case

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Abstract

A simple proof of the Donsker-Varadhan large-deviation principle for occupation measures of Markov process valued in R with discrete time is given. A proof is based on a new version of the Dupui-Ellis large-deviation principle for two-dimensional occupation measures. In our setting, the existence of the invariant measure is not assumed. This condition is replaced (from the point of view of applications) by a more natural one. An example of a Markov process defined by nonlinear recursion, for which sufficient conditions of the existence of the large-deviation principle are easily verified, is given.

Original languageEnglish
Pages (from-to)35-54
Number of pages20
JournalTheory of Probability and its Applications
Volume41
Issue number1
DOIs
StatePublished - Mar 1996

Keywords

  • Exponential tightness
  • Large deviations
  • Local large deviations

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