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Note on Zeifman's bounds on the rate of convergence for birth-death processes

Published online by Cambridge University Press:  14 July 2016

A. Yu. Mitrophanov*
Affiliation:
Saratov State University
*
Postal address: Faculty of Computer Science and Information Technology, Saratov State University, 83 Astrakhanskaya str., Saratov 410012, Russia. Email address: [email protected]

Abstract

It is shown that the method of deriving bounds on the rate of convergence for birth–death processes developed by Zeifman can be effectively applied to stochastic models of chemical reactions.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 2004 

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References

Granovsky, B. L., and Zeifman, A. I. (1997). The decay function of nonhomogeneous birth–death processes, with application to mean-field models. Stoch. Process. Appl. 72, 105120.Google Scholar
Granovsky, B. L., and Zeifman, A. I. (2000). Nonstationary Markovian queues. J. Math. Sci. (New York) 99, 14151438.Google Scholar
Granovsky, B. L., and Zeifman, A. I. (2000). The N-limit of spectral gap of a class of birth–death Markov chains. Appl. Stoch. Models Business Industry 16, 235248.Google Scholar
Mitrophanov, A. Yu. (2003). Stability and exponential convergence of continuous-time Markov chains. J. Appl. Prob. 40, 970979.Google Scholar
Pollett, P. K., and Vassallo, A. (1992). Diffusion approximations for some simple chemical reaction schemes. Adv. Appl. Prob. 24, 875893.Google Scholar
Van Kampen, N. G. (1981). Stochastic Processes in Physics and Chemistry. North Holland, Amsterdam.Google Scholar
Zeifman, A. I. (1991). Some estimates of the rate of convergence for birth and death processes. J. Appl. Prob. 28, 268277.Google Scholar
Zeifman, A. I. (1995). Upper and lower bounds on the rate of convergence for nonhomogeneous birth and death processes. Stoch. Process. Appl. 59, 157173.Google Scholar