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Reversible Markov processes on general spaces and spatial migration processes

Part of: Special processes Markov processes

Published online by Cambridge University Press:  01 July 2016

Richard F. Serfozo
Richard F. Serfozo*
Affiliation:
Georgia Institute of Technology
*
∗ Postal address: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA. Email address: rserfozo@isye.gatech.edu
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Abstract

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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.

Keywords

Reversible Markov processKolmogorov criterionmulticlass birth-death processmobile phonebatch birthbatch death

MSC classification

Primary: 60J75: Jump processes
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 3 , September 2005 , pp. 801 - 818
Copyright
Copyright © Applied Probability Trust 2005 

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