Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-30T19:36:31.218Z Has data issue: false hasContentIssue false
  • English
  • Français

Truncation approximation of the limit probabilities for denumerable semi-Markov processes

Published online by Cambridge University Press:  14 July 2016

Richard L. Tweedie
Richard L. Tweedie*
Affiliation:
Australian National University, Canberra
*
∗Now at CSIRO Division of Mathematics and Statistics, Canberra.
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that methods used by the author to approximate limit probabilities for Markov processes from their Q-matrices extend to semi-Markov processes. The limit probabilities for semi-Markov processes can be approximated using only truncations of the embedded Markov chain transition matrix and the vector of mean holding times.

Keywords

SEMI-MARKOV PROCESSESLIMIT PROBABILITIESERGODIC PROPERTIESJUMP-CHAINFINITE APPROXIMATIONEQUILIBRIUM DISTRIBUTIONSTATIONARY DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 161 - 163
Copyright
Copyright © Applied Probability Trust 1975 

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

Chung, K. L. (1967) Markov Chains with Stationary Transition Probabilities. Springer-Verlag, Berlin.Google Scholar
Çinlar, E. (1969) Markov renewal theory. Adv. Appl. Prob. 1, 123–187.CrossRefGoogle Scholar
Pyke, R. (1961) Markov renewal processes: definitions and preliminary properties. Ann. Math. Statist. 32, 1231–1242.CrossRefGoogle Scholar
Pyke, R. and Schaufele, R. A. (1964) Limit theorems for Markov renewal processes. Ann. Math. Statist. 35, 1746–1764.CrossRefGoogle Scholar
Pyke, R. and Schaufele, R. A. (1966) The existence and uniqueness of stationary measures for Markov renewal processes. Ann. Math. Statist. 37, 1439–1462.CrossRefGoogle Scholar
Tomusyak, A. A. (1972) Computation of ergodic distributions of Markov and semi-Markov processes. Cybernetics 5, (1969), 80–84.CrossRefGoogle Scholar
Tweedie, R. L. (1971) Truncation procedures for non-negative matrices. J. Appl. Prob. 8, 311–320.CrossRefGoogle Scholar
Tweedie, R. L. (1973) The calculation of limit probabilities for denumerable Markov processes from infinitesimal properties. J. Appl. Prob. 10, 84–99.CrossRefGoogle Scholar