Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain

被引：3
|
作者：
Benaim, Michel [1 ]
Champagnat, Nicolas [2 ]
Villemonais, Denis [2 ]
机构：
[1] Univ Neuchatel, Neuchatel, Switzerland
[2] Univ Lorraine, IECL, INRIA, CNRS, F-54000 Nancy, France
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2021年 / 57卷 / 02期
关键词：
Random processes with reinforcement; Stochastic approximation; Pseudo-asymptotic trajectories; Quasi-stationary distributions; EXPONENTIAL CONVERGENCE; SPACES;
D O I：
10.1214/20-AIHP1093
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 a random process with reinforcement, which evolves following the dynamics of a given diffusion process in a bounded domain and is resampled according to its occupation measure when it reaches the boundary. We show that its occupation measure converges to the unique quasi-stationary distribution of the diffusion process absorbed at the boundary of the domain. Our proofs use recent results in the theory of quasi-stationary distributions and stochastic approximation techniques.
引用
收藏
页码：726 / 739
页数：14
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