On the Large Deviation Rate Function for the Empirical Measures of Reversible Jump Markov Processes

Abstract

The large deviations principle for the empirical measure for both continuous and discrete time Markov processes is well known. Various expressions are avail- able for the rate function, but these expressions are usually as the solution to a variational problem, and in this sense not explicit. An interesting class of con- tinuous time, reversible processes was identi ed in the original work of Donsker and Varadhan for which an explicit expression is possible. While this class in- cludes many (reversible) processes of interest, it excludes the case of continuous time pure jump processes, such as a reversible nite state Markov chain. In this paper we study the large deviations principle for the empirical measure of pure jump Markov processes and provide an explicit formula of the rate function under reversibility.

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Document Details

Document Type
Technical Report
Publication Date
Sep 12, 2013
Accession Number
ADA614710

Entities

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  • Paul Dupuis
  • Yufei Liu

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  • Brown University

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DTIC Thesaurus Topics

  • Construction
  • Convergence
  • Distortion
  • Dynamics
  • Generators
  • Guarantees
  • Markov Chains
  • Markov Processes
  • Numbers
  • Probabilistic Models
  • Probability
  • Probability Distributions
  • Random Variables
  • Real Numbers
  • Stochastic Control
  • Two Dimensional
  • Weak Convergence

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