Coupling and harmonic functions in the case of continuous time Markov processes
type: Item
instance of: scholarly article
title: Coupling and harmonic functions in the case of continuous time Markov processes
zbMATH Open document ID: 0845.60075
DOI: 10.1016/0304-4149(95)00055-0
author: Andreas Greven
author: Michael Craig Cranston
published in: Stochastic Processes and their Applications
publication date: 1996-09-02T00:00:00Z
review text: Let \((X^\mu_t)\) and \((X^\nu_t)\), \(t \geq 0\), be continuous-time transient Markov processes taking values in Polish state space with initial distributions \(\mu\) and \(\nu\) and common transition kernel. It is shown that there exist (randomized) stopping times \(S\) and \(T\) for respective processes with the following properties: (i) the distributions of the processes at the stopping times are equal: \(L(X_S^\mu \mid S < \infty) = L(X^\nu_T \mid T < \infty)\); (ii) (maximality property) before coupling (i.e. for \(t < S\), resp. \(t < T\)) the processes move in disjoint subsets of the state space. The proof of the result is based essentially on the potential theoretic approach. Some examples and applications of the result are given. The discrete-time case was considered by the second author earlier [Probab. Theory Relat. Fields 75, 195-212 (1987; Zbl 0596.60070)].
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 31C05
zbMATH DE Number: 859317
zbMATH Keywords: coupling
zbMATH Keywords: Markov process
zbMATH Keywords: potential
zbMATH Keywords: harmonic function
zbMATH Keywords: diffusion
reviewed by: Eugene Kozarovitsky
MaRDI profile type: Publication
full work available at URL: 0304-4149(95)00055-0
OpenAlex ID: W2064731854
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description: scientific article; zbMATH DE number 859317