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Strong ergodicity for Markov processes by coupling methods

Part of: Spectral theory and eigenvalue problems Markov processes

Published online by Cambridge University Press:  14 July 2016

Yong-Hua Mao
Yong-Hua Mao*
Affiliation:
Beijing Normal University
*
∗ Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China. Email address: maoyh@bnu.edu.cn
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Abstract

In this paper, we apply coupling methods to study strong ergodicity for Markov processes, and sufficient conditions are presented in terms of the expectations of coupling times. In particular, explicit criteria are obtained for one-dimensional diffusions and birth-death processes to be strongly ergodic. As a by-product, strong ergodicity implies that the essential spectra of the generators for these processes are empty.

Keywords

Markov semigroupsstrong ergodicitycouplingessential spectrum

MSC classification

Primary: 60J60: Diffusion processes 60J75: Jump processes 35P15: Estimation of eigenvalues, upper and lower bounds
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002 , pp. 839 - 852
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

Research supported in part by RFDP (No. 20010027007), 973 Project, NSFC (10121101) and NSFC for Distinguished Young Scholars (No. 10025105).

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