Law of large numbers and central limit theorem for linear chemical reactions with diffusion. (English) Zbl 0661.60053

Kotelenez, Peter

Ann. Probab. 14, 173-193 (1986).

The models of chemical reaction which take into account the spatial inhomogeneity and the diffusion phenomena are classically of two kinds. The deterministic models are described in terms of partial differential equations, and the stochastic models, based on a space-discretization, are described in terms of space-time jump Markov processes.
The object of this paper is to relate these two kinds of models by a law of large numbers, and to prove a functional central limit theorem.

Reviewer: E.Pardoux

MSC:

60F17	Functional limit theorems; invariance principles
60H15	Stochastic partial differential equations (aspects of stochastic analysis)
60G15	Gaussian processes
60J70	Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)

Keywords:

models of chemical reaction; law of large numbers; functional central limit theorem