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Deterministic limit of the stochastic model of chemical reactions with diffusion

Published online by Cambridge University Press:  01 July 2016

L. Arnold  and
M. Theodosopulu
L. Arnold*
Affiliation:
Universität Bremen
M. Theodosopulu*
Affiliation:
Université Libre de Bruxelles
*
∗Postal address: Fachbereich Mathematik, Universitat Bremen, D-2800 Bremen 33, W. Germany.
∗∗Postal address: Service de Chimie Physique II, Université Libre de Bruxelles, B-1050 Bruxelles, Belgium.
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Abstract

Conditions are given for which the Markov jump process describing the stochastic model of chemical reactions with diffusion converges to the solution of the corresponding deterministic reaction–diffusion equation.

Keywords

REACTION–DIFFUSION EQUATIONSTOCHASTIC MODEL OF CHEMICAL REACTIONS WITH DIFFUSIONAPPROXIMATION OF MARKOV JUMP PROCESSES BY SOLUTIONS OF PDE
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 2 , June 1980 , pp. 367 - 379
Copyright
Copyright © Applied Probability Trust 1980 

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References

1. Brenig, L. and Van Den Broeck, C. (1980) Stochastic Hydrodynamic Theory for One-Component Systems. To appear.CrossRefGoogle Scholar
2. Curtain, R. F. and Pritchard, A. J. (1978) Infinite Dimensional Linear Systems Theory. Lecture Notes in Control and Information Sciences, 8, Springer-Verlag, Berlin.Google Scholar
3. Haken, H. (1978) Synergetics, 2nd edn. Springer-Verlag, Berlin.CrossRefGoogle Scholar
4. Kato, T. (1966) Perturbation Theory for Linear Operators. Springer-Verlag, Berlin.Google Scholar
5. Kuiper, H. J. (1977) Existence and comparison theorems for nonlinear diffusion systems. J. Math. Anal. Appl. 60, 166–181.CrossRefGoogle Scholar
6. Kurtz, T. (1970) Solutions of ordinary differential equations as limits of pure jump Markov processes. J. Appl. Prob. 7, 49–58.CrossRefGoogle Scholar
7. Kurtz, T. (1971) Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Prob. 8, 344–356.CrossRefGoogle Scholar
8. Kurtz, T. (1978) Strong approximation theorems for density dependent Markov chains. Stoch. Proc. Appl. 6, 223–240.CrossRefGoogle Scholar
9. Malek-Mansour, M. (1979) Fluctuations et Transitions de Phase de Nonéquilibre dans les Systèmes Chimiques. Thèse, Université Libre de Bruxelles.Google Scholar
10. Nicolis, G. and Prigogine, I. (1977) Selforganization in Nonequilibrium Systems. Wiley, New York.Google Scholar