Uniform convergence to the Q-process

被引:22
作者
Champagnat, Nicolas [1 ,2 ,3 ]
Villemonais, Denis [1 ,2 ,3 ]
机构
[1] Univ Lorraine, IECL, UMR 7502, Campus Sci,BP 70239, F-54506 Vandoeuvre Les Nancy, France
[2] CNRS, UMR 7502, IECL, F-54506 Vandoeuvre Les Nancy, France
[3] Inria, TOSCA Team, F-54600 Villers Les Nancy, France
来源
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2017年 / 22卷
关键词
quasi-stationary distribution; Q-process; uniform exponential mixing property; conditional ergodic theorem; QUASI-STATIONARY DISTRIBUTIONS;
D O I
10.1214/17-ECP63
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
The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribution of the process. Conversely, we prove that, if a conditioned process converges uniformly to a conservative Markov process which is itself ergodic, then it admits a unique quasi-stationary distribution and converges toward it exponentially fast, uniformly in its initial distribution. As an application, we provide a conditional ergodic theorem.
引用
收藏
页数:7
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