## The Annals of Applied Probability

- Ann. Appl. Probab.
- Volume 2, Number 1 (1992), 131-141.

### Law of Large Numbers in the Supremum Norm for a Chemical Reaction with Diffusion

#### Abstract

A space-time jump Markov process, modeling a chemical reaction with diffusion, is compared in the supremum norm to the usual model, the solution to a partial differential equation. Conditions are given which imply the deviation converges in probability to 0 uniformly on bounded time intervals. Estimates reflecting underlying large deviation behavior are obtained.

#### Article information

**Source**

Ann. Appl. Probab., Volume 2, Number 1 (1992), 131-141.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1177005774

**Digital Object Identifier**

doi:10.1214/aoap/1177005774

**Mathematical Reviews number (MathSciNet)**

MR1143396

**Zentralblatt MATH identifier**

0747.60033

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F17: Functional limit theorems; invariance principles

Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60H05: Stochastic integrals

**Keywords**

Chemical reaction with diffusion law of large numbers density dependent birth and death process

#### Citation

Blount, Douglas. Law of Large Numbers in the Supremum Norm for a Chemical Reaction with Diffusion. Ann. Appl. Probab. 2 (1992), no. 1, 131--141. doi:10.1214/aoap/1177005774. https://projecteuclid.org/euclid.aoap/1177005774