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.
Publié le : 1991-10-14
Classification:
Central limit theorem,
Ornstein-Uhlenbeck process,
stochastic partial differential equation,
reaction diffusion equation,
60F17,
60H15,
60G15
@article{1176990219,
author = {Blount, Douglas},
title = {Comparison of Stochastic and Deterministic Models of a Linear Chemical Reaction with Diffusion},
journal = {Ann. Probab.},
volume = {19},
number = {4},
year = {1991},
pages = { 1440-1462},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990219}
}
Blount, Douglas. Comparison of Stochastic and Deterministic Models of a Linear Chemical Reaction with Diffusion. Ann. Probab., Tome 19 (1991) no. 4, pp. 1440-1462. http://gdmltest.u-ga.fr/item/1176990219/