All Title Author
Keywords Abstract

Mathematics  2010 

Uniqueness in Law for the Allen-Cahn SPDE via Change of Measure

DOI: 10.1016/S0764-4442(00)00190-7

Full-Text   Cite this paper   Add to My Lib


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.


comments powered by Disqus