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Method of Lyapunov functions for analysis of absorption and explosion in Markov chains

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Abstract

The main goal of this paper is to derive some sufficient conditions for testing the absorption, explosion, and nonexplosion of time-inhomogeneous Markov chains with a countable state space. The method of Lyapunov functions is used for this purpose. Several theorems concerned with such sufficient conditions are proved for a general class of Markov chains. Then they are applied to some problems in time-inhomogeneous birth-death processes and branching processes.

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Authors and Affiliations

  1. Wayne State University, Detroit, USA

    P. -L. Chow & R. Z. Khasminskii

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  1. P. -L. Chow
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  2. R. Z. Khasminskii
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Correspondence to P. -L. Chow.

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Original Russian Text © P.-L. Chow, R.Z. Khasminskii, 2011, published in Problemy Peredachi Informatsii, 2011, Vol. 47, No. 3, pp. 19–38.

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Chow, P.L., Khasminskii, R.Z. Method of Lyapunov functions for analysis of absorption and explosion in Markov chains. Probl Inf Transm 47, 232–250 (2011). https://doi.org/10.1134/S0032946011030033

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  • DOI: https://doi.org/10.1134/S0032946011030033

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