Convergence to SPDEs in Stratonovich form (Q1048145)

From the abstract: We consider the perturbation of parabolic operator by large-amplitude highly oscillatory spatially dependent potentials models as Gaussian random fields. The amplitude of the potential is chosen so that the solution to the random equation is affected by the randomness at the leading order. We show that, when the dimension is smaller than the order of the elliptic pseudo-differential operator, the perturbed parabolic equation admits a solution given by a Duhamel expansion. Moreover, as the correlation length of the potential vanishes, we show that the latter solution converges in distribution to the solution of a stochastic parabolic equation with multiplicative noise in proper sense. The theory of mild solutions for such stochastic partial differential equations is developed.