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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:135

Article

Champagnat, Nicolas^1,2,3  Villemonais, Denis^1,2,3 

[1] Univ Lorraine, UMR 7502, IECL, Campus Sci,BP 70239, F-54506 Vandoeuvre Les Nancy, France

[2] CNRS, IECL, UMR 7502, F-54506 Vandoeuvre Les Nancy, France

[3] INRIA, TOSCA Team, F-54600 Villers Les Nancy, France

关键词: Stochastic Lotka-Volterra systems;    Multidimensional birth and death process;    Process absorbed on the boundary;    Quasi-stationary distribution;    Uniform exponential mixing property;    Lyapunov function;   

DOI  :  10.1016/j.spa.2020.12.005

来源: Elsevier

【 摘 要 】

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. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free