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A Diffusion Approximation for Markov Renewal Processes

  • Steven P. Clark (a1) and Peter C. Kiessler (a2)

Abstract

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.

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Copyright

Corresponding author

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

References

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[1] Billingsley, P. (1999). Convergence of Probability Measures. John Wiley, New York.
[2] Çinlar, E. (1975). Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, NJ.
[3] Durrett, R. (1991). Probability: Theory and Examples. Wadsworth and Brooks, Pacific Grove, CA.
[4] Keilson, J. and Wishart, D. M. G. (1964). A central limit theorem for processes defined on a Markov chain. Proc. Camb. Philos. Soc. 60, 547567.
[5] Limnios, N. and Oprişan, G. (2001). Semi-Markov Processes and Reliability. Birkhäuser, Boston, MA.
[6] Lindvall, T. (1992). Lectures on the Coupling Method. John Wiley, New York.
[7] Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability. Springer, New York.
[8] Pitman, J. W. (1974). Uniform rates of convergence for Markov chain transition probabilities. Z. Wahrscheinlichkeitsth. 29, 193227.
[9] Resnick, S. I. (1992). Adventures in Stochastic Processes. Birkhäuser, Boston, MA.
[10] Whitt, W. (2002). Stochastic-Process Limits. Springer, New York.
[11] Whitt, W. (2002). Stochastic-Process Limits. Internet Supplement.

Keywords

MSC classification

A Diffusion Approximation for Markov Renewal Processes

  • Steven P. Clark (a1) and Peter C. Kiessler (a2)

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