Cranston M, Greven A (1995)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1995
Publisher: Elsevier
Book Volume: 60
Pages Range: 261-286
Journal Issue: 2
URI: https://www.sciencedirect.com/science/article/pii/0304414995000550?via=ihub
DOI: 10.1016/0304-4149(95)00055-0
Consider two transient Markov processes (X ), (X ) with the same transition semigroup and initial distributions v and μ. The probability spaces supporting the processes each are also assumed to support an exponentially distributed random variable independent of the process. We show that there exist (randomized) stopping times S for (X ), T for (X ) with common final distribution, L(X |S < ∞) = L(X |T < ∞), and the property that for t < S, resp. t < T, the processes move in disjoint portions of the state space. For such a coupling (S, T) it is shown Prob(S=∝)+Prob(T=∝)= max hε{lunate}Hh′≤1〈y-μh〉. where H denotes the bounded harmonic functions of the Markov transition semigroup. Extensions, consequences and applications of this result are discussed. © 1995.
APA:
Cranston, M., & Greven, A. (1995). Coupling and harmonic functions in the case of continuous time Markov processes. Stochastic Processes and their Applications, 60(2), 261-286. https://dx.doi.org/10.1016/0304-4149(95)00055-0
MLA:
Cranston, Michael, and Andreas Greven. "Coupling and harmonic functions in the case of continuous time Markov processes." Stochastic Processes and their Applications 60.2 (1995): 261-286.
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