Reversible Markov processes on general spaces and spatial migration processes
Richard F. Serfozo
Source: Adv. in Appl. Probab. Volume 37, Number 3
(2005), 801-818.
Abstract
In this study, we characterize the equilibrium behavior of spatial migration processes that represent population migrations, or birth-death processes, in general spaces. These processes are reversible Markov jump processes on measure spaces. As a precursor, we present fundamental properties of reversible Markov jump processes on general spaces. A major result is a canonical formula for the stationary distribution of a reversible process. This involves the characterization of two-way communication in transitions, using certain Radon-Nikodým derivatives. Other results concern a Kolmogorov criterion for reversibility, time reversibility, and several methods of constructing or identifying reversible processes.
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Keywords: Reversible Markov process; Kolmogorov criterion; multiclass birth-death process; mobile phone; batch birth; batch death
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1127483748
Digital Object Identifier: doi:10.1239/aap/1127483748
Mathematical Reviews number (MathSciNet): MR2156561
Zentralblatt MATH identifier: 1074.60091
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