%0 Journal Article
%T Uniqueness in Law for the Allen-Cahn SPDE via Change of Measure
%A Hassan Allouba
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/S0764-4442(00)00190-7
%X We start by first using change of measure to prove the transfer of uniqueness in law among pairs of parabolic SPDEs differing only by a drift function, under an almost sure $L^2$ condition on the drift/diffusion ratio. This is a considerably weaker condition than the usual Novikov one, and it allows us to prove uniqueness in law for the Allen-Cahn SPDE driven by space-time white noise with diffusion function $a(t,x,u)=Cu^\gamma$, $1/2\le\gamma\le1$ and $C\ne0$. The same transfer result is also valid for ordinary SDEs and hyperbolic SPDEs.
%U http://arxiv.org/abs/1005.3766v1