Displaying similar documents to “Some results for the reflection problems in Hilbert spaces”

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 .

Stochastic viability and a comparison theorem

Anna Milian (1995)

Colloquium Mathematicae

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We give explicit necessary and sufficient conditions for the viability of polyhedrons with respect to Itô equations. Using the viability criterion we obtain a comparison theorem for multi-dimensional Itô processes

Existence and uniqueness of solutions for non-linear stochastic partial differential equations.

Tomás Caraballo Garrido (1991)

Collectanea Mathematica

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We state some results on existence and uniqueness for the solution of non linear stochastic PDEs with deviating arguments. In fact, we consider the equation dx(t) + (A(t,x(t)) + B(t,x(a(t))) + f(t)dt = (C(t,x(b(t)) + g(t))dwt, where A(t,·), B(t,·) and C(t,·) are suitable families of non linear operators in Hilbert spaces, wt is a Hilbert valued Wiener process, and a, b are functions of delay. If A satisfies a coercivity condition and a monotonicity hypothesis, and if B, C are Lipschitz...

Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces

Marco Fuhrman (1995)

Studia Mathematica

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We consider a semigroup acting on real-valued functions defined in a Hilbert space H, arising as a transition semigroup of a given stochastic process in H. We find sufficient conditions for analyticity of the semigroup in the L 2 ( μ ) space, where μ is a gaussian measure in H, intrinsically related to the process. We show that the infinitesimal generator of the semigroup is associated with a bilinear closed coercive form in L 2 ( μ ) . A closability criterion for such forms is presented. Examples are...

Some properties of superprocesses under a stochastic flow

Kijung Lee, Carl Mueller, Jie Xiong (2009)

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

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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.