SPDEs with pseudodifferential generators: the existence of a density

Samy Tindel

Displaying similar documents to “SPDEs with pseudodifferential generators: the existence of a density”

Malliavin calculus for two-parameter processes

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

Zdzisław Brzeźniak, Szymon Peszat (1999)

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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.

Existence of density for the solution to the three-dimensional wave equation.

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We study regularity of stochastic convolutions solving Volterra equations on $R^{d}$ 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)

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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.

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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...