Reversible Markov processes on general spaces and spatial migration processes
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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.
1972 ◽
Vol 23
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pp. 32-46
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2014 ◽
Vol 90
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pp. 136-139
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1996 ◽
Vol 64
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pp. 257-271
2015 ◽
Vol 143
(18)
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pp. 184105
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1990 ◽
Vol 26
(10)
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pp. 1193-1200
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2018 ◽
Vol 57
(6)
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pp. 890-906
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2013 ◽
Vol 150
(1)
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pp. 181-203
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