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January, 1986 Law of Large Numbers and Central Limit Theorem for Linear Chemical Reactions with Diffusion
Peter Kotelenez
Ann. Probab. 14(1): 173-193 (January, 1986). DOI: 10.1214/aop/1176992621

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.

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Peter Kotelenez. "Law of Large Numbers and Central Limit Theorem for Linear Chemical Reactions with Diffusion." Ann. Probab. 14 (1) 173 - 193, January, 1986. https://doi.org/10.1214/aop/1176992621

Information

Published: January, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0661.60053
MathSciNet: MR815964
Digital Object Identifier: 10.1214/aop/1176992621

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

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 1 • January, 1986
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