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arXiv · 1005.3766

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

Hassan Allouba
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Abstract

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 $a(t,x,u)=Cu^γ$, $1/2\leγ\le1$ and $C\ne0$. The same transfer result is also valid for ordinary SDEs and hyperbolic SPDEs.

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BibTeXRIS

Hassan Allouba. 2010-05-20. Uniqueness in Law for the Allen-Cahn SPDE via Change of Measure. https://doi.org/10.1016/s0764-4442(00)00190-7

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