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 -