Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-13T03:38:50.467Z Has data issue: false hasContentIssue false
  • English
  • Français

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: spclark@email.uncc.edu
∗∗ Postal address: Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA. Email address: kiesslp@clemson.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 

References

Billingsley, P. (1999). Convergence of Probability Measures. John Wiley, New York.Google Scholar
Çinlar, E. (1975). Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Durrett, R. (1991). Probability: Theory and Examples. Wadsworth and Brooks, Pacific Grove, CA.Google Scholar
Keilson, J. and Wishart, D. M. G. (1964). A central limit theorem for processes defined on a Markov chain. Proc. Camb. Philos. Soc. 60, 547–567.Google Scholar
Limnios, N. and Oprişan, G. (2001). Semi-Markov Processes and Reliability. Birkhäuser, Boston, MA.CrossRefGoogle Scholar
Lindvall, T. (1992). Lectures on the Coupling Method. John Wiley, New York.Google Scholar
Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability. Springer, New York.Google Scholar
Pitman, J. W. (1974). Uniform rates of convergence for Markov chain transition probabilities. Z. Wahrscheinlichkeitsth. 29, 193–227.Google Scholar
Resnick, S. I. (1992). Adventures in Stochastic Processes. Birkhäuser, Boston, MA.Google Scholar
Whitt, W. (2002). Stochastic-Process Limits. Springer, New York.CrossRefGoogle Scholar
Whitt, W. (2002). Stochastic-Process Limits. Internet Supplement.Google Scholar