Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T07:52:23.038Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
∗∗ Postal address: Department of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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