Geodesic
SPDEs with pseudodifferential generators: the existence of a density
Applicationes Mathematicae, Tome 27 (2000) no. 3, pp. 287-308.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/am-27-3-287-308
Keywords: pseudodifferential operators, stochastic partial differential equations, Malliavin's calculus

Samy Tindel 1

1 
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Samy Tindel. SPDEs with pseudodifferential generators: the existence of a density. Applicationes Mathematicae, Tome 27 (2000) no. 3, pp. 287-308. doi : 10.4064/am-27-3-287-308. http://geodesic.mathdoc.fr/articles/10.4064/am-27-3-287-308/

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