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Conditions for strong ergodicity using intensity matrices

Published online by Cambridge University Press:  14 July 2016

Jean Johnson  and
Dean Isaacson
Jean Johnson*
Affiliation:
University of Kansas
Dean Isaacson*
Affiliation:
Iowa State University
*
∗ Postal address: Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA.
∗∗ Postal address: Department of Statistics, Iowa State University, Ames, IA 50011, USA.
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Abstract

Sufficient conditions for strong ergodicity of discrete-time non-homogeneous Markov chains have been given in several papers. Conditions have been given using the left eigenvectors ψn of Pn(ψ nPn = ψ n) and also using the limiting behavior of Pn. In this paper we consider the analogous results in the case of continuous-time Markov chains where one uses the intensity matrices Q(t) instead of P(s, t). A bound on the rate of convergence of certain strongly ergodic chains is also given.

Keywords

NON-HOMOGENEITYCONTINUOUS-TIME MARKOV CHAINS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 34 - 42
Copyright
Copyright © Applied Probability Trust 1988 

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References

[1] Anily, S. and Federgruen, A. (1985) Ergodicity in parametric non-stationary Markov chains: an application to simulated annealing methods. Operat. Res. To appear.Google Scholar
[2] Anily, S. and Federgruen, A. (1987) Simulated annealing methods with general acceptance probabilities. J. Appl. Prob. 24, 657–667.CrossRefGoogle Scholar
[3] Cinlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
[4] Gidas, B. (1985) Nonstationary markov chains and convergence of the annealing algorithm. J. Statist. Phys. 39, 73–131.CrossRefGoogle Scholar
[5] Griffeath, D. (1975) Uniform coupling of nonhomogeneous Markov chains. J. Appl. Prob. 12, 753–763.Google Scholar
[6] Huang, C., Isaacson, D. and Vinograde, B. (1976) The rate of convergence of nonhomogeneous Markov chains. Z. Wahrscheinlichkeitsth. 35, 141–146.Google Scholar
[7] Iosifescu, M. (1980) Finite Markov Processes and Their Applications. Wiley, Bucharest.Google Scholar
[8] Isaacson, D. and Madsen, R. (1976) Markov Chains: Theory and Applications. Wiley, New York.Google Scholar
[9] Johnson, J. (1984) Ergodic Properties of Nonhomogeneous, Continuous-time Markov Chains. Ph.D. Dissertation, Iowa State University.Google Scholar
[10] Madsen, R. and Isaacson, D. (1973) Strongly ergodic behavior for nonstationary Markov processes. Ann. Prod. 1, 329–335.Google Scholar
[11] Mitra, D., Romeo, F. and Sangiovanni-Vincentelli, A. (1986) Convergence and finite-time behavior of simulated annealing. Adv. Appl. Prob. 18, 747–771.Google Scholar
[12] Mott, J. L. (1957) Conditions for ergodicity of non-homogeneous, finite Markov chains. Proc. R. Soc. Edinburgh 64, 369–380.Google Scholar
[13] Paz, A. P. (1971) Introduction to Probabilistic Automata. Academic Press, New York.Google Scholar