Malliavin calculus for two-parameter processes
D. Nualart, M. Sanz (1985)
Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
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Displaying similar documents to “SPDEs with pseudodifferential generators: the existence of a density”
Malliavin calculus for two-parameter processes
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 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 -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.
Existence of density for the solution to the three-dimensional wave equation.
Lluís Quer-Sardanyons, Marta Sanz-Solé (2003)
RACSAM
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We prove existence of density for the real-valued solution to a 3-dimensional stochastic wave equation (...).
Stochastic differential equations in Hilbert spaces
Anna Chojnowska-Michalik (1979)
Banach Center Publications
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Regularity of solutions to stochastic Volterra equations
Anna Karczewska, Jerzy Zabczyk (2000)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We study regularity of stochastic convolutions solving Volterra equations on driven by a spatially homogeneous Wiener process. General results are applied to stochastic parabolic equations with fractional powers of Laplacian.
Strong solutions for stochastic differential equations with jumps
Zenghu Li, Leonid Mytnik (2011)
Annales de l'I.H.P. Probabilités et statistiques
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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.
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...