The Annals of Probability

Law of Large Numbers and Central Limit Theorem for Linear Chemical Reactions with Diffusion

Peter Kotelenez

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Abstract

Two mathematical models of chemical reactions with diffusion for a single reactant in a one-dimensional volume are compared, namely, the deterministic and the stochastic models. The deterministic model is given by a partial differential equation, the stochastic one by a space-time jump Markov process. By the law of large numbers the consistency of the two models is proved. The deviation of the stochastic model from the deterministic model is estimated by a central limit theorem. This limit is a distribution-valued Gauss-Markov process and can be represented as the mild solution of a certain stochastic partial differential equation.

Article information

Source
Ann. Probab., Volume 14, Number 1 (1986), 173-193.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992621

Digital Object Identifier
doi:10.1214/aop/1176992621

Mathematical Reviews number (MathSciNet)
MR815964

Zentralblatt MATH identifier
0661.60053

JSTOR
links.jstor.org

Keywords
60 F17 60 H15 60 G15 60 J70 Reaction and diffusion equation thermodynamic limit central limit theorem stochastic partial differential equation semigroup approach

Citation

Kotelenez, Peter. Law of Large Numbers and Central Limit Theorem for Linear Chemical Reactions with Diffusion. Ann. Probab. 14 (1986), no. 1, 173--193. doi:10.1214/aop/1176992621. https://projecteuclid.org/euclid.aop/1176992621


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