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

Daehong Kim () and Yoichi Oshima
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Daehong Kim: Faculty of Engineering, Kumamoto University
Yoichi Oshima: Faculty of Engineering, Kumamoto University

Journal of Theoretical Probability, 2010, vol. 23, issue 1, 148-168

Abstract: 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.

Keywords: Dirichlet forms; Poincaré-type inequality; Recurrent process; Simulated annealing; Time-inhomogeneous diffusion processes; 60J60; 60J45; 60H30; 31C25 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-008-0196-0

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