## The Annals of Probability

- Ann. Probab.
- Volume 16, Number 2 (1988), 700-716.

### Central Limit Theorem for an Infinite Lattice System of Interacting Diffusion Processes

#### Abstract

A central limit theorem for interacting diffusion processes is shown. The proof is based on an infinite-dimensional stochastic integral representation of smooth functionals of diffusion processes. Exponential decay of correlations and the equation of the fluctuation field are also obtained.

#### Article information

**Source**

Ann. Probab., Volume 16, Number 2 (1988), 700-716.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176991781

**Digital Object Identifier**

doi:10.1214/aop/1176991781

**Mathematical Reviews number (MathSciNet)**

MR929072

**Zentralblatt MATH identifier**

0652.60059

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60J60: Diffusion processes [See also 58J65] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

**Keywords**

Central limit theorem for interacting stochastic systems stochastic differential equation in infinite dimensions stochastic integral representation Haussmann formula

#### Citation

Deuschel, Jean-Dominique. Central Limit Theorem for an Infinite Lattice System of Interacting Diffusion Processes. Ann. Probab. 16 (1988), no. 2, 700--716. doi:10.1214/aop/1176991781. https://projecteuclid.org/euclid.aop/1176991781