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

Tomás Caraballo Garrido

Displaying similar documents to “Existence and uniqueness of solutions for non-linear stochastic partial differential equations.”

On the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane's stochastic integral equations.

Adrian Constantin (1994)

Publicacions Matemàtiques

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In this paper we use the Schauder fixed point theorem and methods of integral inequalities in order to prove a result on the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane stochastic integral equations.

Non-linear stochastic partial differential equations with delays: existence and uniqueness of solutions.

Tomás Caraballo Garrido (1991)

Extracta Mathematicae

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The main aim of this paper is to study stochastic PDE's with delay terms. In fact, we prove existence and uniqueness of solutions (in Itô's sense) for a rather general type of stochastic PDE's with non-linear monotone operators and with delays.

An operator-valued stochastic integral, III

D. Kannan (1972)

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

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Stochastic differential equations in Hilbert spaces

Anna Chojnowska-Michalik (1979)

Banach Center Publications

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Hilbert-valued anticipating stochastic differential equations

Axel Grorud, David Nualart, Marta Sanz-Solé (1994)

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

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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

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 $(t, x) \in [0, T] \times 𝒪$ is absolutely continuous with respect to the Lebesgue measure.

Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process

Zdzisław Brzeźniak, Szymon Peszat (1999)

Studia Mathematica

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Stochastic partial differential equations on $ℝ^{d}$ are considered. The noise is supposed to be a spatially homogeneous Wiener process. Using the theory of stochastic integration in Banach spaces we show the existence of a Markovian solution in a certain weighted $L^{q}$ -space. Then we obtain the existence of a space continuous solution by means of the Da Prato, Kwapień and Zabczyk factorization identity for stochastic convolutions.

Stochastic differential inclusions

Michał Kisielewicz (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The definition and some existence theorems for stochastic differential inclusions depending only on selections theorems are given.