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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:87

Article

Fuh, CD ; Zhang, CH

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

DOI  :  10.1016/S0304-4149(99)00104-0

来源: Elsevier

【 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.

【 授权许可】

Free