Poisson equation, moment inequalities and quick convergence for Markov random walks

被引：14

作者：

Fuh, CD ^{[1
]}

Zhang, CH

机构：

[1] Acad Sinica, Inst Stat Sci, Taipei 11529, Taiwan

[2] Rutgers State Univ, Hill Ctr, Dept Stat, Piscataway, NJ 08854 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2000年 / 87卷 / 01期

基金：

美国国家科学基金会;

关键词：

inequality; Markov random walk; tail probability; moment; Poisson equation; quick convergence; Wald equation; renewal theory;

D O I：

10.1016/S0304-4149(99)00104-0

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 provide moment inequalities and sufficient conditions for the quick convergence for Markov random walks, without the assumption of uniform ergodicity for the underlying Markov chain. Our approach is based on martingales associated with the Poisson equation and Wald equations for the second moment with a variance formula. These results are applied to nonlinear renewal theory for Markov random walks. A random coefficient autoregression model is investigated as an example. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: primary 60G40; secondary 60J10.

引用

页码：53 / 67

页数：15

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