WELL-POSEDNESS OF FOKKER–PLANCK TYPE EQUATIONS ON THE WIENER SPACE

DOI10.1142/S0219025710004061zbMath1200.60042MaRDI QIDQ3580210

De Jun Luo

Publication date: 11 August 2010

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

zbMATH Keywords

stochastic differential equationFokker-Planck equationMalliavin calculuscommutator estimate

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) Initial value problems for second-order parabolic equations (35K15) Fokker-Planck equations (35Q84)

Related Items

Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients ⋮ Quantitative stability estimates for Fokker-Planck equations ⋮ Lagrangian flows driven by \(BV\) fields in Wiener spaces

Cites Work

• Unnamed Item
• Equations différentielles sur l'espace de Wiener et formules de Cameron- Martin non-linéaires
• Wasserstein space over the Wiener space
• Ordinary differential equations, transport theory and Sobolev spaces
• 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
• Fokker-Planck equations and maximal dissipativity for Kolmogorov operators with time dependent singular drifts in Hilbert spaces
• Absolutely continuous flows generated by Sobolev class vector fields in finite and infinite dimensions
• Renormalized solutions of some transport equations with partially \(W^{1,1}\) velocities and applications
• Anticipating flows on the Wiener space generated by vector fields of low regularity
• Uniqueness of solutions to weak parabolic equations for measures
• Existence of solutions to weak parabolic equations for measures