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1 results

  • Reversible Markov processes on general spaces and spatial migration processes

  • Part of
  • Richard F. Serfozo
  • Journal:
    Advances in Applied Probability / Volume 37 / Issue 3 / September 2005
    Published online by Cambridge University Press:
    01 July 2016, pp. 801-818
    Print publication:
    September 2005
    • Article
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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.