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

Abstract

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 $a(t,x,u)=C{u}^{\gamma }$, with $C\ne 0$ and $1/2\le \gamma <1$.

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