The Annals of Probability
- Ann. Probab.
- Volume 19, Number 4 (1991), 1440-1462.
Comparison of Stochastic and Deterministic Models of a Linear Chemical Reaction with Diffusion
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.
Ann. Probab., Volume 19, Number 4 (1991), 1440-1462.
First available in Project Euclid: 19 April 2007
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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