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Diffusion approximations for some simple chemical reaction schemes

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

P. K. Pollett  and
A. Vassallo
P. K. Pollett*
Affiliation:
The University of Queensland
A. Vassallo
Affiliation:
The University of Queensland
*
∗Postal address: Department of Mathematics, The University of Queensland, QLD 4072, Australia.
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Abstract

We shall establish functional limit laws for the concentration of the various species in simple chemical reactions. These results allow us to conclude that, under quite general conditions, the concentration has an approximate normal distribution. We provide estimates for the mean and the variance which are valid at all stages of the reaction, in particular, the non-equilibrium phase. We also provide a detailed comparison of our results with the earlier work of Dunstan and Reynolds ([7], [8]).

Keywords

MARKOV CHAINS: STOCHASTIC MODELS: CHEMICAL KINETICS

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 4 , December 1992 , pp. 875 - 893
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

∗∗

Present address: SUNCORP Insurance and Finance Ltd., G.P.O. Box 1453, Brisbane, QLD 4001, Australia.

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