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

Nicolas Champagnat and Denis Villemonais

Stochastic Processes and their Applications, 2021, vol. 135, issue C, 51-74

Abstract: We study the uniform convergence to quasi-stationarity 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 an original non-linear Lyapunov criterion involving two functions, which applies to general Markov processes.

Keywords: Stochastic Lotka–Volterra systems; Multidimensional birth and death process; Process absorbed on the boundary; Quasi-stationary distribution; Uniform exponential mixing property; Lyapunov function (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2020.12.005

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