Uniform convergence to the Q-process
Uniform convergence to the Q-process
复制标题
统一收敛到 Q 过程
DOI：
10.1214/17-ecp63
复制
发表时间：
2016
影响因子：
0.5
通讯作者：
D. Villemonais
中科院分区：
文献类型：
--
作者：
Nicolas Champagnat;D. Villemonais
本文的第一个目的是在一个有条件的过程的准平稳分布的适当假设下，量化该过程向其q过程的收敛速度。相反地，我们证明了，如果一个条件过程一致收敛于一个本身是遍历的保守马尔可夫过程，那么它承认一个唯一的拟平稳分布，并且在它的初始分布中匀速地向它收敛。作为应用，我们给出了一个条件遍历定理。
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.