SPDEs with pseudodifferential generators: the existence of a density
Volume 27 / 2000
Applicationes Mathematicae 27 (2000), 287-308
DOI: 10.4064/am-27-3-287-308
Abstract
We consider the equation du(t,x)=Lu(t,x)+b(u(t,x))dtdx+σ(u(t,x))dW(t,x) where t belongs to a real interval [0,T], x belongs to an open (not necessarily bounded) domain $\mathcal O$, and L is a pseudodifferential operator. We show that under sufficient smoothness and nondegeneracy conditions on L, the law of the solution u(t,x) at a fixed point $(t,x)\in [0,T] \times \mathcal O$ is absolutely continuous with respect to the Lebesgue measure.
