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A Diffusion Approximation for Markov Renewal Processes

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Steven P. Clark  and
Peter C. Kiessler
Steven P. Clark*
Affiliation:
University of North Carolina at Charlotte
Peter C. Kiessler*
Affiliation:
Clemson University
*
∗ Postal address: Department of Finance and Business Law, University of North Carolina at Charlotte, 9201 University City Boulevard, Charlotte, NC 28075, USA. Email address: [email protected]
∗∗ Postal address: Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA. Email address: [email protected]
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Abstract

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For a Markov renewal process where the time parameter is discrete, we present a novel method for calculating the asymptotic variance. Our approach is based on the key renewal theorem and is applicable even when the state space of the Markov chain is countably infinite.

Keywords

Markov renewal processfunctional central limit theoremasymptotic variance

MSC classification

Primary: 60G10: Stationary processes
Secondary: 60F17: Functional limit theorems; invariance principles
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 366 - 378
Copyright
Copyright © Applied Probability Trust 2007 

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