Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients

DOI10.4171/RMI/711zbMath1262.60056arXiv1002.4297MaRDI QIDQ1941166

Xicheng Zhang

Publication date: 11 March 2013

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.4297

zbMATH Keywords

large deviationHardy-Littlewood maximal functiongeneralized stochastic flowDiPerna-Lions theory

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Large deviations (60F10) Fokker-Planck equations (35Q84)

Related Items (19)

Strong solutions to stochastic differential equations with rough coefficients ⋮ The Itô SDEs and Fokker–Planck equations with Osgood and Sobolev coefficients ⋮ Convergence rate of the EM algorithm for SDEs with low regular drifts ⋮ Stochastic differential equations with Sobolev drifts and driven by \(\alpha\)-stable processes ⋮ On a maximal inequality and its application to SDEs with singular drift ⋮ Estimate of transition kernel for Euler-Maruyama scheme for SDEs driven by \(\alpha\)-stable noise and applications ⋮ Stochastic Lagrangian perturbation of Lie transport and applications to fluids ⋮ On the pathwise uniqueness for a class of degenerate Itô-stochastic differential equations ⋮ Quasi-invariance of the stochastic flow associated to Itô's SDE with singular time-dependent drift ⋮ Stochastic Lagrangian path for Leray's solutions of 3D Navier-Stokes equations ⋮ Quantitative stability estimates for Fokker-Planck equations ⋮ Singular Brownian diffusion processes ⋮ Existence and uniqueness of degenerate SDEs with Hölder diffusion and measurable drift ⋮ Uniqueness problems for degenerate Fokker-Planck-Kolmogorov equations ⋮ Central limit theorem and moderate deviation principle for McKean-Vlasov SDEs ⋮ Schauder estimates for nonlocal kinetic equations and applications ⋮ Support theorem for stochastic differential equations with Sobolev coefficients ⋮ Optimal stability estimates and a new uniqueness result for advection-diffusion equations ⋮ Regularization effects of a noise propagating through a chain of differential equations: an almost sharp result

Cites Work

• Unnamed Item
• Unnamed Item
• Equations différentielles ordinaires: Non explosion et mesures quasi- invariantes
• Transport equation and Cauchy problem for BV vector fields
• Ordinary differential equations, transport theory and Sobolev spaces
• Large deviations for infinite dimensional stochastic dynamical systems
• Transport equations and quasi-invariant flows on the Wiener space
• Stochastic differential equations with coefficients in Sobolev spaces
• On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions
• A variational representation for certain functionals of Brownian motion
• Large deviations for small noise diffusions with discontinuous statistics
• Flows associated with irregular \(\mathbb R^d\)-vector fields
• Estimates and regularity results for the DiPerna-Lions flow

This page was built for publication: Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients