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

被引：21

作者：

Champagnat, Nicolas ^{[1
,2
,3
]}

Villemonais, Denis ^{[1
,2
,3
]}

机构：

[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

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2021年 / 135卷

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; QUASI-STATIONARY DISTRIBUTIONS; ONE-DIMENSIONAL DIFFUSIONS; EXPONENTIAL CONVERGENCE; STOCHASTIC-PROCESSES; MODELS;

D O I：

10.1016/j.spa.2020.12.005

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：51 / 74

页数：24

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