Reversible Markov processes on general spaces and spatial migration processes

Richard F. Serfozo
2002 Advances in Applied Probability  
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
more » ... 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.
doi:10.1239/aap/1127483748 fatcat:wn7qaujo6rekhb2gug2oxqwfkm