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

Authors
Fuh, CD Zhang, CH
Citation
Cd. Fuh et Ch. Zhang, Poisson equation, moment inequalities and quick convergence for Markov random walks, STOCH PR AP, 87(1), 2000, pp. 53-67
Citations number
20
Categorie Soggetti
Mathematics
Journal title
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
ISSN journal
03044149 → ACNP
Volume
87
Issue
1
Year of publication
2000
Pages
53 - 67
Database
ISI
SICI code
0304-4149(200005)87:1<53:PEMIAQ>2.0.ZU;2-M
Abstract
We provide moment inequalities and sufficient conditions for the quick conv ergence for Markov random walks, without the assumption of uniform ergodici ty for the underlying Markov chain. Our approach is based on martingales as sociated with the Poisson equation and Wald equations for the second moment with a variance formula. These results are applied to nonlinear renewal th eory for Markov random walks. A random coefficient autoregression model is investigated as an example. (C) 2000 Elsevier Science B.V. All rights reser ved. MSC: primary 60G40; secondary 60J10.