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Additive Functionals for Discrete-Time Markov Chains with Applications to Birth-Death Processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Yuanyuan Liu
Yuanyuan Liu*
Affiliation:
Central South University
*
∗ Postal address: School of Mathematics, Railway Campus, Central South University, Changsha, Hunan, 410075, China. Email address: [email protected]
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Abstract

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In this paper we are interested in bounding or calculating the additive functionals of the first return time on a set for discrete-time Markov chains on a countable state space, which is motivated by investigating ergodic theory and central limit theorems. To do so, we introduce the theory of the minimal nonnegative solution. This theory combined with some other techniques is proved useful for investigating the additive functionals. This method is used to study the functionals for discrete-time birth-death processes, and the polynomial convergence and a central limit theorem are derived.

Keywords

Additive functionalbirth-death processergodicitycentral limit theorem

MSC classification

Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J55: Local time and additive functionals
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 4 , December 2011 , pp. 925 - 937
Copyright
Copyright © Applied Probability Trust 2011 

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