An approximation result for a quasi-linear stochastic heat equation

We study the limiting behavior, as nn goes to ∞∞, of a solution of a stochastic partial differential equation driven by a process XnXn which converges in law to the Brownian sheet. Under some assumptions, we prove that the solution unun converges in distribution in C([0,1]2)C([0,1]2) to a weak solution of a SPDE.