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Displaying similar documents to “Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn–Hilliard equation”

Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II

Viorel Barbu, Giuseppe Da Prato, Luciano Tubaro (2011)

Annales de l'I.H.P. Probabilités et statistiques

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This work is concerned with the existence and regularity of solutions to the Neumann problem associated with a Ornstein–Uhlenbeck operator on a bounded and smooth convex set of a Hilbert space . This problem is related to the reflection problem associated with a stochastic differential equation in .

SPDEs with pseudodifferential generators: the existence of a density

Samy Tindel (2000)

Applicationes Mathematicae

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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 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 ) ∈ [ 0 , T ] × 𝒪 is absolutely continuous with respect to the Lebesgue measure.