SPDEs law equivalence and the compact support property: applications to the Allen-Cahn SPDE

Details SPDEs law equivalence and the compact support property: applications to the Allen-Cahn SPDE SPDEs law equivalence and the compact support property: applications to the Allen-Cahn SPDE

2010-05-20

arxiv.org/abs/1005.3800v1

C. R. Acad. Sci. Paris S\'er. I Math. 331 (2000), no. 3, 245-250

Mathematics

Probability

6 pages, 2/9 papers from my 2000-2006 collection (preprint version)

Scientific paper

10.1016/S0764-4442(00)01625-6

Using our uniqueness in law transfer result for SPDEs, described in a recent note, we prove the equivalence of laws of SPDEs differing by a drift, under vastly applicable conditions. This gives us the equivalence in the compact support property among a large class of SPDEs. As an important application, we prove the equivalence in law of the Allen-Cahn and the associated heat SPDEs; and we give a criterion for the compact support property to hold for the Allen-Cahn SPDE with diffusion function $a(t,x,u)=Cu^\gamma$, with $C\ne0$ and $ 1/2\le\gamma<1$.

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