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Fluctuations near homogeneous states of chemical reactions with diffusion

Published online by Cambridge University Press:  01 July 2016

Peter Kotelenez
Peter Kotelenez*
Affiliation:
Universität Bremen
*
∗Postal address: Forschungsschwerpunkt Dynamische Systeme, Universität Bremen, Bibliothekstrasse, Postfach 330440, 2800 Bremen 33, W. Germany.
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Abstract

Conditions are given under which a space-time jump Markov process describing the stochastic model of non-linear chemical reactions with diffusion converges to the homogeneous state solution of the corresponding reaction-diffusion equation. The deviation is measured by a central limit theorem. This limit is a distribution-valued Ornstein–Uhlenbeck process and can be represented as the mild solution of a certain stochastic partial differential equation.

Keywords

REACTION-DIFFUSION EQUATIONSTOCHASTIC MODEL OF NON-LINEAR CHEMICAL REACTIONS WITH DIFFUSIONTHERMODYNAMIC LIMITCENTRAL LIMIT THEOREMHIGH DENSITY LIMITSTOCHASTIC PARTIAL DIFFERENTIAL EQUATION
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 2 , June 1987 , pp. 352 - 370
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

This research was done during the author&s stay at the University of North Carolina at Chapel Hill in April 1985 and was supported by the Air force Office of Scientific Research under AFOSR Grant No. F 49620 82 C 0009.

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