Malliavin and flow regularity of SDEs. Application to the study of densities and the stochastic transport equation

DOI10.1080/17442508.2015.1102265zbMath1337.60115arXiv1410.0786OpenAlexW2286086841MaRDI QIDQ2804559

Torstein Nilssen, David R. Baños

Publication date: 4 May 2016

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.0786

zbMATH Keywords

Brownian motionstochastic differential equationsstrong solutionsdensitiesSobolev regularitystochastic transport equationMalliavin regularity

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) White noise theory (60H40) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (3)

Hölder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients ⋮ The Bismut-Elworthy-Li formula for mean-field stochastic differential equations ⋮ Computing deltas without derivatives

Cites Work

• A variational approach to the construction and Malliavin differentiability of strong solutions of SDEs
• Riesz transform and integration by parts formulas for random variables
• Stochastic homeomorphism flows of SDEs with singular drifts and Sobolev diffusion coefficients
• Well-posedness of the transport equation by stochastic perturbation
• Construction of strong solutions of SDE's via Malliavin calculus
• Existence of densities of solutions of stochastic differential equations by Malliavin calculus
• Dirichlet forms and analysis on Wiener space
• Integration with respect to local time
• Sobolev differentiable stochastic flows for SDEs with singular coefficients: applications to the transport equation
• Existence and regularity of density for solutions to stochastic differential equations with boundary conditions
• The Malliavin Calculus and Related Topics
• Malliavin Calculus with Applications to Stochastic Partial Differential Equations

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