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October, 1991 Comparison of Stochastic and Deterministic Models of a Linear Chemical Reaction with Diffusion
Douglas Blount
Ann. Probab. 19(4): 1440-1462 (October, 1991). DOI: 10.1214/aop/1176990219


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.


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Douglas Blount. "Comparison of Stochastic and Deterministic Models of a Linear Chemical Reaction with Diffusion." Ann. Probab. 19 (4) 1440 - 1462, October, 1991.


Published: October, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0741.92022
MathSciNet: MR1127711
Digital Object Identifier: 10.1214/aop/1176990219

Primary: 60F17
Secondary: 60G15 , 60H15

Keywords: central limit theorem , Ornstein-Uhlenbeck process , reaction diffusion equation , Stochastic partial differential equation

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 4 • October, 1991
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