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 , 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 is absolutely continuous with respect to the Lebesgue measure.
@article{bwmeta1.element.bwnjournal-article-zmv27i3p287bwm,
author = {Samy Tindel},
title = {SPDEs with pseudodifferential generators: the existence of a density},
journal = {Applicationes Mathematicae},
volume = {27},
year = {2000},
pages = {287-308},
zbl = {0998.60062},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv27i3p287bwm}
}
Tindel, Samy. SPDEs with pseudodifferential generators: the existence of a density. Applicationes Mathematicae, Tome 27 (2000) pp. 287-308. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv27i3p287bwm/
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