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Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes

Abstract : We study the quasi-stationary behavior of multidimensional processes absorbed when one of the coordinates vanishes. Our results cover competitive or weakly cooperative Lotka-Volterra birth and death processes and Feller diffusions with competitive Lotka-Volterra interaction. To this aim, we develop original non-linear Lyapunov criteria involving two Lyapunov functions, which apply to general Markov processes.
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https://hal.inria.fr/hal-01503697
Contributor : Nicolas Champagnat Connect in order to contact the contributor
Submitted on : Monday, February 1, 2021 - 4:46:48 PM
Last modification on : Saturday, October 16, 2021 - 11:18:03 AM

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Nicolas Champagnat, Denis Villemonais. Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes. Stochastic Processes and their Applications, Elsevier, 2021, 135, pp.51-74. ⟨10.1016/j.spa.2020.12.005⟩. ⟨hal-01503697v2⟩

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