On Stein's method for stochastically monotone single-birth chains

被引：0
|
作者：
Daly, Fraser [1 ,2 ]
机构：
[1] Heriot Watt Univ, Dept Actuarial Math & Stat, Edinburgh EH14 4AS, Scotland
[2] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Scotland
来源：
STATISTICS & PROBABILITY LETTERS | 2024年 / 206卷
关键词：
Markov chain; Poisson's equation; Stochastic monotonicity; Total variation distance; Stein's method; AUGMENTED TRUNCATION APPROXIMATIONS; STATIONARY DISTRIBUTIONS; MARKOV-CHAINS;
D O I：
10.1016/j.spl.2023.109993
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 discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's equation for such a process. Applications include rates of convergence to stationarity, and bounding the total variation distance between the stationary distributions of two Markov chains in the case where one transition matrix dominates the other.
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页数：6
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