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Path integrals for continuous-time Markov chains

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

P. K. Pollett  and
V. T. Stefanov
P. K. Pollett*
Affiliation:
University of Queensland
V. T. Stefanov*
Affiliation:
University of Western Australia
*
∗ Postal address: Department of Mathematics, University of Queensland, Brisbane, QLD 4072, Australia. Email address: pkp@maths.uq.edu.au
∗∗ Postal address: Department of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia.
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Abstract

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

Keywords

Hitting timesextinction timespopulation processes

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002 , pp. 901 - 904
Copyright
Copyright © Applied Probability Trust 2002 

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References

[1]. Anderson, W. (1991). Continuous-Time Markov Chains: An Applications-Oriented Approach. Springer, New York.Google Scholar
[2]. Ball, F., and Stefanov, V. (2001). Further approaches to computing fundamental characteristics of birth–death processes. J. Appl. Prob./ 38, 995–1005.Google Scholar
[3]. Di Crescenzo, A. (1998). First-passage-time densities and avoiding probabilities for birth-and-death processes with symmetric sample paths. J. Appl. Prob./ 35, 383–394.CrossRefGoogle Scholar
[4]. Flajolet, P., and Guillemin, F. (2000). The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions. Adv. Appl. Prob./ 32, 750–778.Google Scholar
[5]. Hernández-Suárez, C., and Castillo-Chavez, C. (1999). A basic result on the integral for birth–death Markov processes. Math. Biosci./ 161, 95–104.Google Scholar
[6]. McNeil, D. (1970). Integral functionals of birth and death processes and related limiting distributions. Ann. Math. Statist./ 41, 480–485.Google Scholar
[7]. Pollett, P., and Stefanov, V. (2002). Path integrals for continuous-time Markov chains. Tech. Rep., Department of Mathematics, University of Queensland. Available at http://www.maths.uq.edu.au~pkp.Google Scholar
[8]. Rubino, G., and Sericola, B. (1989). Sojourn times in finite Markov processes. J. Appl. Prob./ 27, 744–756.Google Scholar
[9]. Stefanov, V., and Wang, S. (2000). A note on integrals for birth–death processes. Math. Biosci./ 168, 161–165.Google Scholar
[10]. Syski, R. (1992). Passage Times for Markov Chains. IOS Press, Amsterdam.Google Scholar