posted on 2005-08-22, 14:48authored byA.L. Piatnitski, Huaizhong Zhao, W.A. Zheng
In this paper, we consider a class of multi-dimensional SPDEs of
parabolic type with space-time white noise. We discretize the spacetime
white noise to independently identically distributed time white
noise located on configuration space and seek the solution to the nonlinear
SPDE with such a family of discretized time noises. Then we
prove that the laws of the above solutions are tight when the sum over
the configuration space of the above family of time noises tends to spacetime
white noise. Finally we show that any limitingla w satisfies the
desired SPDE.