UC Irvine

In this paper, we consider multi-dimensional SPDEs of parabolic type with space-time white noise. We discretize the space-time white noise to independently identically distributed time white noise located on configuration space and then consider the convergence of the discretized solution u(ti xi n). We first prove that in general the laws of u(ti xi n)dtdx form a tight sequence and the limit is the law of some measure-valued random variable which gives a weak integral solution in the linear case. For the stochastic multi-dimensional KPP equation, we prove that the solution is real-valued. This is the first example of SPDEs discovered so far in multi-dimensions with real-valued solutions.