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Solutions to a class of multidimensional SPDES
preprintposted on 2005-08-22, 14:48 authored by A.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.
- Mathematical Sciences
NotesThis is a pre-print.