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

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

2010-05-20

arxiv.org/abs/1005.3766v1

C. R. Acad. Sci. Paris S\'er. I Math. 330 (2000), no. 5, 371-376

Mathematics

Probability

6 pages, 1/9 papers of my 2000-2006 collection (preprint version)

Scientific paper

10.1016/S0764-4442(00)00190-7

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.

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