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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.
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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 

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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