Cerrai, Sandra, A Khasminskii type averaging principle for stochastic reaction.diffusion equations, Annals of applied probability , 19(3), 2009, pp. 899-948
We prove that an averaging principle holds for a general class of stochastic reaction.diffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a finite number of degrees of freedom can be extended to infinite-dimensional systems.