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Quasi-stationarity and quasi-ergodicity of general Markov processes

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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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Correspondence to ShouMei Li.

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Zhang, J., Li, S. & Song, R. Quasi-stationarity and quasi-ergodicity of general Markov processes. Sci. China Math. 57, 2013–2024 (2014). https://doi.org/10.1007/s11425-014-4835-x

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  • DOI: https://doi.org/10.1007/s11425-014-4835-x

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