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Journal Articles Stochastic Processes and their Applications Year : 2021

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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Dates and versions

hal-01503697 , version 1 (07-04-2017)
hal-01503697 , version 2 (01-02-2021)

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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, 2021, 135, pp.51-74. ⟨10.1016/j.spa.2020.12.005⟩. ⟨hal-01503697v2⟩
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