Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients

DOI10.1016/j.crma.2010.01.001zbMath1202.60112OpenAlexW1980923880MaRDI QIDQ964441

Xicheng Zhang, Michael Roeckner

Publication date: 15 April 2010

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2010.01.001

zbMATH Keywords

stochastic differential equationsweak solutionsuniqueness of solutionsFokker-Planck equationsdegenerate coefficients

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Fokker-Planck equations (35Q84)

Related Items (20)

Optimal control of stochastic differential equations via Fokker-Planck equations ⋮ On the Cauchy problem for Fokker-Planck-Kolmogorov equations with potential terms on arbitrary domains ⋮ Strong solutions to stochastic differential equations with rough coefficients ⋮ Uniqueness for solutions of Fokker-Planck equations related to singular SPDE driven by Lévy and cylindrical Wiener noise ⋮ On uniqueness of solutions to the Cauchy problem for degenerate Fokker-Planck-Kolmogorov equations ⋮ The Itô SDEs and Fokker–Planck equations with Osgood and Sobolev coefficients ⋮ \(L^p\)-solutions of Fokker-Planck equations ⋮ On the martingale problem for degenerate-parabolic partial differential operators with unbounded coefficients and a mimicking theorem for Itô processes ⋮ Strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type ⋮ Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients ⋮ Superposition principle for non-local Fokker-Planck-Kolmogorov operators ⋮ On the uniqueness of integrable and probability solutions to the Cauchy problem for the Fokker-Planck-Kolmogorov equations ⋮ On uniqueness problems related to the Fokker-Planck-Kolmogorov equation for measures ⋮ Quantitative stability estimates for Fokker-Planck equations ⋮ A unified treatment for ODEs under Osgood and Sobolev type conditions ⋮ On the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to Fokker-Planck-Kolmogorov equations ⋮ Statistical Stability for Transport in Random Media ⋮ Stochastic Hamiltonian flows with singular coefficients ⋮ Uniqueness problems for degenerate Fokker-Planck-Kolmogorov equations ⋮ Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stochastic flows of SDEs with irregular coefficients and stochastic transport equations
• Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients
• Estimates and regularity results for the DiPerna-Lions flow
• Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients
• Uniqueness of solutions to weak parabolic equations for measures

This page was built for publication: Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients