The Annals of Applied Probability

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

Douglas Blount

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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


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