Stochastic Systems Seminar
Abstract: We are concerned with the validity of the averaging principle for a general class of stochastic PDE's of reaction-diffusion type, having multiplicative noise, in any space dimension. We extend the classical Khasminskii approach for systems with a finite number of degrees of freedom to infinite dimensional systems. All coefficients in the slow motion equation are assumed to depend on the fast variable, and hence we have averaging both in the reaction and in the diffusion coefficient. We also study the fluctuations of the slow motion from the averaged motion and we prove a central limit theorem for the normalized difference.