Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density

zbMath1193.60081arXivmath/0610769MaRDI QIDQ964011

Lahcen Boulanba, Mohamed Mellouk, M'hamed Eddahbi

Publication date: 14 April 2010

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610769

zbMATH Keywords

Malliavin calculusfractional derivative operatorGaussian noise white in time and correlated in space

Mathematics Subject Classification ID

Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

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Cites Work

• Unnamed Item
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• Unnamed Item
• On the martingale problem for generators of stable processes with perturbations
• Some properties of superprocesses under a stochastic flow
• Fractional kinetic equation for Hamiltonian chaos
• Stochastic partial differential equations for some measure-valued diffusions
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The law of the solution to a nonlinear hyperbolic SPDE
• Global solution and smoothing effect for a non-local regularization of a hyperbolic equation.
• Comparison results and steady states for the Fujita equation with fractional Laplacian.
• A probabilistic approach for nonlinear equations involving the fractional Laplacian and a singular operator
• A stochastic wave equation in two space dimensions: smoothness of the law
• Growing fractal interfaces in the presence of self-similar hopping surface diffusion
• On stochastic partial differential equations with spatially correlated noise: smoothness of the law.
• Existence and smoothness of the density for spatially homogeneous SPDEs
• Distributions in the physical and engineering sciences. Vol. 1: Distributional and fractal calculus, integral transforms and wavelets
• On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension
• Regularity of the sample paths of a class of second-order SPDE's
• On a stochastic partial differential equation with non-local diffusion
• The Malliavin Calculus and Related Topics
• Global and Exploding Solutions for Nonlocal Quadratic Evolution Problems
• Blow-up of semilinear pde’s at the critical dimension. A probabilistic approach
• Burgers equation with a fractional derivative; hereditary effects on nonlinear acoustic waves
• Corrections to: Extending the martingale measure stochastic integral with applications to spatially homogeneous s. p. d. e. 's
• Stochastic Equations in Infinite Dimensions