Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces

DOI10.1007/s00028-010-0058-yzbMath1239.34063arXiv0907.1431OpenAlexW2125335896MaRDI QIDQ423419

Giuseppe Da Prato, Vladimir I. Bogachev, Michael Roeckner

Publication date: 2 June 2012

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.1431

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Diffusion processes (60J60) Ordinary differential equations and systems with randomness (34F05) Transport processes in time-dependent statistical mechanics (82C70) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Transition functions, generators and resolvents (60J35) Applications of operator theory in probability theory and statistics (47N30)

Related Items (22)

Path-Based Divergence Rates and Lagrangian Uncertainty in Stochastic Flows ⋮ Uniqueness for solutions of Fokker-Planck equations related to singular SPDE driven by Lévy and cylindrical Wiener noise ⋮ Adaptive Galerkin approximation algorithms for Kolmogorov equations in infinite dimensions ⋮ A cost on paths of measures which induces the Fokker-Planck equation ⋮ Lévy flows and associated stochastic PDEs ⋮ Uniqueness of Fokker-Planck equations for SPIN lattice systems. I: compact case ⋮ Perelman's \(W\)-entropy for the Fokker-Planck equation over complete Riemannian manifolds ⋮ Uniqueness of Fokker-Planck equations for spin lattice systems. II: Non-compact case ⋮ Uniqueness for continuity equations in Hilbert spaces with weakly differentiable drift ⋮ A natural order in dynamical systems based on Conley-Markov matrices ⋮ Characterizing Gaussian flows arising from Itô's stochastic differential equations ⋮ Lagrangian Uncertainty Quantification and Information Inequalities for Stochastic Flows ⋮ Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces ⋮ Fokker-Planck equations for SPDE with non-trace-class noise ⋮ Kolmogorov equations for randomly perturbed generalized Newtonian fluids ⋮ On the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to Fokker-Planck-Kolmogorov equations ⋮ Strong uniqueness for SDEs in Hilbert spaces with nonregular drift ⋮ A mild Itô formula for SPDEs ⋮ Uniqueness for Solutions of Fokker–Planck Equations on Infinite Dimensional Spaces ⋮ Fokker–Planck equation for dissipative 2D Euler equations with cylindrical noise ⋮ A note on stochastic semilinear equations and their associated Fokker-Planck equations ⋮ Remarks on Stochastic Navier-Stokes Equations

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