Quasi-stationarity and quasi-ergodicity of general Markov processes |
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Authors: | JunFei Zhang ShouMei Li RenMing Song |
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Affiliation: | 1. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, China 2. Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA
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Abstract: | In this paper, we study the quasi-stationarity and quasi-ergodicity of general Markov processes. We show, among other things, that if X is a standard Markov process admitting a dual with respect to a finite measure m and if X admits a strictly positive continuous transition density p(t, x, y) (with respect to m) which is bounded in (x, y) for every t > 0, then X has a unique quasi-stationary distribution and a unique quasi-ergodic distribution. We also present several classes of Markov processes satisfying the above conditions. |
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Keywords: | Markov processes quasi-stationary distributions mean ratio quasi-stationary distributions quasiergodicity distributions |
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