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On Quasi-Stationary distributions in absorbing discrete-time finite Markov chains

  • J. N. Darroch (a1) and E. Seneta (a2)
Abstract

The time to absorption from the set T of transient states of a Markov chain may be sufficiently long for the probability distribution over T to settle down in some sense to a “quasi-stationary” distribution. Various analogues of the stationary distribution of an irreducible chain are suggested and compared. The reverse process of an absorbing chain is found to be relevant.

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COPYRIGHT: © Sheffield: Applied Probability Trust 
References
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[1] Bartlett, M. S. (1960) Stochastic Population Models. Methuen, London.
[2] Ewens, W. J. (1963) The diffusion equation and a pseudo-distribution in genetics. J. R. Statist. Soc. B 25, 405–412.
[3] Kemeny, J. G. and Snell, L. J. (1960) Finite Markov Chains. Van Nostrand, Princeton, New Jersey.
[4] Bhat, B. R. (1961) Some properties of regular Markov chains. Ann. Math. Statist. 32, 59–71.
[5] Gantmacher, F. R. (1959) Applications of the Theory of Matrices. Interscience, New York.
[6] Feller, W. (1957) Introduction to Probability Theory and its Applications. John Wiley, New York.
[7] Mandl, P. (1959) Sur le comportement asymptotique des probabilités dans les ensembles des états d'une chaîne de Markov homogène. (in Russian) Casopis Pest. Mat. 84, 140–149.
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Journal of Applied Probability
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