吸收的随机单调马氏链的拟平稳分布（英文）

Quasi-stationary distributions for absorbing stochastically monotone Markov chains

本文考虑吸收的随机单调马氏链在生存时间内的某些极限定理.主要考虑三种类型的拟平稳分布:平稳条件的拟平稳分布、双重极限条件的拟平稳分布和极限条件平均比值的拟平稳分布.研究了随机单调马氏链的三类拟平稳分布的唯一性和吸引域问题.在某种条件下,这三类拟平稳分布都是唯一的,并且所有的初始分布都在这个唯一的拟平稳分布的吸引域里面.最后,将主要结论应用到生灭过程.

In this paper,we prove some limit theorems for absorbing stochastically monotone Markov chain during its lifetime.The emphases are on the stationary conditional,doubly limiting conditional and limiting conditional mean ratio quasi-stationary distributions.We study the uniqueness and domain of attraction of three types of quasi-stationary distributions for stochastically monotone Markov chains.A sufficient condition for the uniqueness of the three types of quasi-stationary distributions is given in our main results and under this condition,the unique quasi-stationary distribution attracts all initial distributions.We apply the main results to birth and death processes.