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Conditions Under Which a Markov Chain Converges to its Steady State in Finite Time

Published online by Cambridge University Press:  27 July 2009

Peter W. Glynn  and
Donald L. Iglehart
Peter W. Glynn
Affiliation:
Department of Operations Research Stanford University, Stanford, CA 94305
Donald L. Iglehart
Affiliation:
Department of Operations Research Stanford University, Stanford, California 94305
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Abstract

Analysis of the initial transient problem of Monte Carlo steady-state simulation motivates the following question for Markov chains: when does there exist a deterministic Tsuch that P{X(T) = y|(0) = x} = ®(y), where ρ is the stationary distribution of X? We show that this can essentially never happen for a continuous-time Markov chain; in discrete time, such processes are i.i.d. provided the transition matrix is diagonalizable.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 3 , July 1988 , pp. 377 - 382
Copyright
Copyright © Cambridge University Press 1988

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References

Cinlar, E. (1975). Introduction to stochastic processes. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Ethier, S.N. & Kurtz, T.G. (1986). Markov processes: Characterization and convergence. New York: John Wiley.CrossRefGoogle Scholar
Feller, W. (1968). An introduction to probability theory and its applications, Vol. 1. New York: John Wiley.Google Scholar
Lancaster, P. (1969). Theory of matrices. New York: Academic Press.Google Scholar
Schiuben, L. (1983). Confidence interval estimation using standardized time series. Operations Research 31: 1090–1108.Google Scholar
Subelman, E.J. (1976). On the class of Markov chains with finite convergence time. Stochastic Processes Applications 4: 253–259.CrossRefGoogle Scholar