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

Cheng Der Fuh; Cun Hui Zhang

doi:10.1016/S0304-4149(99)00104-0

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

Cheng Der Fuh, Cun Hui Zhang

School of Arts and Sciences, Statistics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	53-67
Number of pages	15
Journal	Stochastic Processes and their Applications
Volume	87
Issue number	1
DOIs	https://doi.org/10.1016/S0304-4149(99)00104-0
State	Published - May 2000

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Keywords

Inequality
Markov random walk
Moment
Poisson equation
Primary 60G40
Quick convergence
Renewal theory
Secondary 60J10
Tail probability
Wald equation

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10.1016/S0304-4149(99)00104-0

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

abstract = "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.",

keywords = "Inequality, Markov random walk, Moment, Poisson equation, Primary 60G40, Quick convergence, Renewal theory, Secondary 60J10, Tail probability, Wald equation",

author = "Fuh, {Cheng Der} and Zhang, {Cun Hui}",

note = "Funding Information: The research of Cheng-Der Fuh was partially supported by the NSC 87-2118-M-001-003. The research of Cun-Hui Zhang was partially supported by the National Science Foundation of USA and the National Security Agency of USA. The authors also would like to thank the referees, who provided many helpful comments on an earlier draft. ",

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T1 - Poisson equation, moment inequalities and quick convergence for Markov random walks

AU - Fuh, Cheng Der

AU - Zhang, Cun Hui

N1 - Funding Information: The research of Cheng-Der Fuh was partially supported by the NSC 87-2118-M-001-003. The research of Cun-Hui Zhang was partially supported by the National Science Foundation of USA and the National Security Agency of USA. The authors also would like to thank the referees, who provided many helpful comments on an earlier draft.

PY - 2000/5

Y1 - 2000/5

N2 - 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.

AB - 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.

KW - Inequality

KW - Markov random walk

KW - Moment

KW - Poisson equation

KW - Primary 60G40

KW - Quick convergence

KW - Renewal theory

KW - Secondary 60J10

KW - Tail probability

KW - Wald equation

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DO - 10.1016/S0304-4149(99)00104-0

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SN - 0304-4149

VL - 87

SP - 53

EP - 67

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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