## The Annals of Probability

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

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

#### 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