Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-14T12:40:40.028Z Has data issue: false hasContentIssue false
  • English
  • Français

Proportional intensities and strong ergodicity for Markov processes

Published online by Cambridge University Press:  14 July 2016

Mark Scott  and
Dean L. Isaacson
Mark Scott*
Affiliation:
Mayo Clinic
Dean L. Isaacson*
Affiliation:
Iowa State University
*
∗ Postal address: Department of Medical Statistics and Epidemiology, Mayo Clinic, Rochester, MN 55901, U.S.A.
∗∗ Postal address: Departments of Mathematics and Statistics, Iowa State University, Ames, IA 50011, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

By assuming the proportionality of the intensity functions at each time point for a continuous-time non-homogeneous Markov process, strong ergodicity for the process is determined through strong ergodicity of a related discrete-time Markov process. For processes having proportional intensities, strong ergodicity implies having the limiting matrix L satisfy L · P(s, t) = L, where P(s, t) is the matrix of transition functions.

Keywords

MARKOV PROCESSSTRONG ERGODICITYPROPORTIONAL HAZARDS
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 185 - 190
Copyright
Copyright © Applied Probability Trust 1983 

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] Chiang, C. L. (1980) An Introduction to Stochastic Processes and their Applications. Krieger, New York.Google Scholar
[2] Fix, E. and Neyman, J. (1951) A simple stochastic model of recovery, relapse, death and loss of patients. Human Biol. 23, 205–241.Google ScholarPubMed
[3] Isaacson, D. and Arnold, B. (1978) Strong ergodicity for continuous-time Markov chains. J. Appl. Prob. 15, 699–706.CrossRefGoogle Scholar
[4] Isaacson, D. and Madsen, D. (1976) Markov Chains. Wiley, New York.Google Scholar
[5] Kendall, D. G. (1948) On the generalized birth-and-death process. Ann. Math. Statist. 19, 1–15.Google Scholar
[6] Scott, M. (1979) Characterizations of Strong Ergodicity for Continuous-Time Markov Chains. Ph.D. Dissertation, Iowa State University, Ames.Google Scholar
[7] Tweedie, R. L. (1981) Criteria for ergodicity, exponential ergodicity and strong ergodicity of Markov processes. J. Appl. Prob. 18, 122–130.Google Scholar
[8] Yong, P. L. (1976) Some results related to Q-bounded Markov processes. Nanta Math. 8, 34–41.Google Scholar