On existence of limiting distribution for time-nonhomogeneous countable Markov process

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/235003

Title: On existence of limiting distribution for time-nonhomogeneous countable Markov process
Author(s): Abramov, V.; Liptser, R.
Abstract: In this paper, sufficient conditions are given for the existence of limiting distribution of a nonho-mogeneous countable Markov chain with time-dependent transition intensity matrix. The method of proof exploits the fact that if the distribution of random process Q = (Qtt≥0 (is absolutely continuous with)respect to the distribution of ergodic random process Qo = (Qtot≥0, then (Formula presented), where π is the invariant measure of Qo. We apply this result for asymptotic analysis, as t → ∞, of a nonhomogeneous countable Markov chain which shares limiting distribution with an ergodic birth-and-death process.
Publication type: Journal article
Source: Queueing Systems, Vol. 46, no. 3-4 (Mar 2004), pp. 353-361
Publication year: 2004
FOR Code(s): 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0104 Statistics
Keyword(s): Birth-and-death process; Countable Markov process; Existence of the limiting distribution
Publisher: Springer
ISSN: 0257-0130
Publisher URL: http://dx.doi.org/10.1023/B:QUES.0000027990.74497.b2
Peer reviewed