On the construction and Malliavin differentiability of solutions of Lévy noise driven SDE's with singular coefficients

DOI10.1016/j.jfa.2014.02.009zbMath1300.60079arXiv1305.2043OpenAlexW2010424281MaRDI QIDQ2253286

Sven Haadem, Frank Norbert Proske

Publication date: 25 July 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.2043

zbMATH Keywords

Lévy processesMalliavin calculusstrong solutions of SDE'sYamada-Watanabe principle

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (15)

Strong rate of convergence for the Euler-Maruyama approximation of SDEs with Hölder continuous drift coefficient ⋮ Construction of Malliavin differentiable strong solutions of SDEs under an integrability condition on the drift without the Yamada-Watanabe principle ⋮ Strong solutions to stochastic equations with a Lévy noise and a non-constant diffusion coefficient ⋮ Ergodicity of stochastic differential equations with jumps and singular coefficients ⋮ Strong existence and uniqueness for stable stochastic differential equations with distributional drift ⋮ Strong solutions to stochastic equations with Lévy noise and a discontinuous drift coefficient ⋮ On weak solutions of SDEs with singular time-dependent drift and driven by stable processes ⋮ Restoration of well-posedness of infinite-dimensional singular ODE's via noise ⋮ Strong existence and higher order Fréchet differentiability of stochastic flows of fractional Brownian motion driven SDEs with singular drift ⋮ Unnamed Item ⋮ Regularity properties of the stochastic flow of a skew fractional Brownian motion ⋮ Tightness and weak convergence of probabilities on the Skorokhod space on the dual of a nuclear space and applications ⋮ Strong convergence of the Euler-Maruyama approximation for a class of Lévy-driven SDEs ⋮ Regularity properties of jump diffusions with irregular coefficients ⋮ Gradient estimates and ergodicity for SDEs driven by multiplicative Lévy noises via coupling

Cites Work

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• Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift
• A variational approach to the construction and Malliavin differentiability of strong solutions of SDEs
• Pathwise uniqueness for singular SDEs driven by stable processes
• Hitchhiker's guide to the fractional Sobolev spaces
• Tightness of probabilities on C([0,1;\(S_ p\)) and D([0,1];\(S_ p\))]
• Random perturbation of PDEs and fluid dynamic models. École d'Été de Probabilités de Saint-Flour XL -- 2010
• Systems of equations driven by stable processes
• Well-posedness of the transport equation by stochastic perturbation
• Potential theory of truncated stable processes
• Construction of strong solutions of SDE's via Malliavin calculus
• Stochastic differential equations with jumps
• Uniqueness in law for pure jump Markov processes
• Strong solutions of stochastic equations with singular time dependent drift
• Perturbation theory for linear operators.
• Perturbation of drift-type for Levy processes
• On stochastic differential equations driven by a Cauchy process and other stable Lévy motions
• Diffusion approximation of nuclear space-valued stochastic differential equations driven by Poisson random measures
• Existence of strong solutions for Itô's stochastic equations via approximations
• Stochastic differential equations driven by stable processes for which pathwise uniqueness fails
• On Stochastic Differential Equations with Locally Unbounded Drift
• The Malliavin Calculus and Related Topics
• Lévy Processes and Stochastic Calculus
• On Strong Solutions of Stochastic Equations with Degenerate Coefficients
• On the Strong Solutions of Stochastic Differential Equations
• Estimates of Fourier transforms in Sobolev spaces
• Singular Elliptic Operators of Second Order with Purely Discrete Spectra
• On one-dimensional stochastic differential equations driven by stable processes
• A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT

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