A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations
Daniel Ocone, Etienne Pardoux (1989)
Annales de l'I.H.P. Probabilités et statistiques
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A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations
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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.
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