Bounds and Asymptotics for the Rate of Convergence of Birth-Death Processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 1, pp. 18-38
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The first part of the paper is a review; it describes the proposed approach and gives the general basis of the method constructed by one of the authors in the 1990's in order to obtain estimates and explicit representations for the rates of convergence for birth-death processes. The second part of the paper presents new results obtained with the described method, which has been applied to specific classes of birth-death processes related to mean-field models and the $M/M/N/N+R$ queueing system related to the asymptotic behavior of the rate of convergence in the case when the number of states of the process tends to infinity.
Keywords:
rate of convergence, birth-death processes, mean-field models, Charlier polynomial, queueing system.
@article{TVP_2009_54_1_a1,
author = {E. van Doorn and A. I. Zeifman and T. L. Panfilova},
title = {Bounds and {Asymptotics} for the {Rate} of {Convergence} of {Birth-Death} {Processes}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {18--38},
publisher = {mathdoc},
volume = {54},
number = {1},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2009_54_1_a1/}
}
TY - JOUR AU - E. van Doorn AU - A. I. Zeifman AU - T. L. Panfilova TI - Bounds and Asymptotics for the Rate of Convergence of Birth-Death Processes JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2009 SP - 18 EP - 38 VL - 54 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2009_54_1_a1/ LA - ru ID - TVP_2009_54_1_a1 ER -
%0 Journal Article %A E. van Doorn %A A. I. Zeifman %A T. L. Panfilova %T Bounds and Asymptotics for the Rate of Convergence of Birth-Death Processes %J Teoriâ veroâtnostej i ee primeneniâ %D 2009 %P 18-38 %V 54 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_2009_54_1_a1/ %G ru %F TVP_2009_54_1_a1
E. van Doorn; A. I. Zeifman; T. L. Panfilova. Bounds and Asymptotics for the Rate of Convergence of Birth-Death Processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 1, pp. 18-38. http://geodesic.mathdoc.fr/item/TVP_2009_54_1_a1/