A stochastic evolution equation arising from the fluctuations of a class of interacting particle systems

Abstract

In an earlier paper, we studied the approximation of solutions V(t) to a class of SPDEs by the empirical measure Vⁿ(t) of a system of n interacting diffusions. In the present paper, we consider a central limit type problem, showing that \sqrt{n}(Vⁿ-V )n converges weakly, in the dual of a nuclear space, to the unique solution of a stochastic evolution equation. Analogous results in which the di.usions that determine Vⁿ are replaced by their Euler approximations are also discussed.