The Annals of Probability

Comparison of Stochastic and Deterministic Models of a Linear Chemical Reaction with Diffusion

Douglas Blount

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Abstract

Particles placed in $N$ cells on the unit interval give birth or die according to linear rates. Adjacent cells are coupled by diffusion with a rate proportional to $N^2$. Cell numbers are divided by a density parameter to represent concentrations, and the resulting space-time Markov process is compared to a corresponding deterministic model, the solution to a partial differential equation. The models are viewed as Hilbert space valued processes and compared by means of a law of large numbers and central limit theorem. New and nearly optimal results are obtained by exploiting the Ornstein-Uhlenbeck type structure of the stochastic model.

Article information

Source
Ann. Probab., Volume 19, Number 4 (1991), 1440-1462.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990219

Digital Object Identifier
doi:10.1214/aop/1176990219

Mathematical Reviews number (MathSciNet)
MR1127711

Zentralblatt MATH identifier
0741.92022

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60H15: Stochastic partial differential equations [See also 35R60] 60G15: Gaussian processes

Keywords
Central limit theorem Ornstein-Uhlenbeck process stochastic partial differential equation reaction diffusion equation

Citation

Blount, Douglas. Comparison of Stochastic and Deterministic Models of a Linear Chemical Reaction with Diffusion. Ann. Probab. 19 (1991), no. 4, 1440--1462. doi:10.1214/aop/1176990219. https://projecteuclid.org/euclid.aop/1176990219


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