TY - JOUR

T1 - On existence of limiting distribution for time-nonhomogeneous countable Markov process

AU - Abramov, V.

AU - Liptser, R.

PY - 2004

Y1 - 2004

N2 - 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 = (Qt t≥0 (is absolutely continuous with)respect to the distribution of ergodic random process Qo = (Qto t≥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.

AB - 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 = (Qt t≥0 (is absolutely continuous with)respect to the distribution of ergodic random process Qo = (Qto t≥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.

KW - Birth-and-death process

KW - Countable Markov process

KW - Existence of the limiting distribution

UR - http://www.scopus.com/inward/record.url?scp=3543132404&partnerID=8YFLogxK

U2 - 10.1023/b:ques.0000027990.74497.b2

DO - 10.1023/b:ques.0000027990.74497.b2

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AN - SCOPUS:3543132404

SN - 0257-0130

VL - 46

SP - 353

EP - 361

JO - Queueing Systems

JF - Queueing Systems

IS - 3-4

ER -