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Some Inequalities Related to Transience and Recurrence of Markov Processes and Their Applications

Author

Listed:
  • Daehong Kim

    (Faculty of Engineering, Kumamoto University)

  • Yoichi Oshima

    (Faculty of Engineering, Kumamoto University)

Abstract

For an irreducible symmetric Markov process on a (not necessarily compact) state space associated with a symmetric Dirichlet form, we give Poincaré-type inequalities. As an application of the inequalities, we consider a time-inhomogeneous diffusion process obtained by a time-dependent drift transformation from a diffusion process and give general conditions for the transience or recurrence of some sets. As a particular case, the diffusion process appearing in the theory of simulated annealing is considered.

Suggested Citation

  • Daehong Kim & Yoichi Oshima, 2010. "Some Inequalities Related to Transience and Recurrence of Markov Processes and Their Applications," Journal of Theoretical Probability, Springer, vol. 23(1), pages 148-168, March.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:1:d:10.1007_s10959-008-0196-0
    DOI: 10.1007/s10959-008-0196-0
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