The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions”

Strong solutions for stochastic differential equations with jumps

Zenghu Li, Leonid Mytnik (2011)

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

Similarity:

General stochastic equations with jumps are studied. We provide criteria for the uniqueness and existence of strong solutions under non-Lipschitz conditions of Yamada–Watanabe type. The results are applied to stochastic equations driven by spectrally positive Lévy processes.

SPDEs with pseudodifferential generators: the existence of a density

Samy Tindel (2000)

Applicationes Mathematicae

Similarity:

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.

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

Similarity:

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 .

Some properties of superprocesses under a stochastic flow

Kijung Lee, Carl Mueller, Jie Xiong (2009)

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

Similarity:

For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov’s -theory for linear SPDE.