Weak solutions to Vlasov–McKean equations under Lyapunov-type conditions

DOI10.1142/S0219493719500424zbMath1434.60216arXiv1901.07778OpenAlexW2914028148MaRDI QIDQ5213054

Wilhelm Stannat, Sima Mehri

Publication date: 31 January 2020

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.07778

zbMATH Keywords

Lyapunov methodGirsanov theoremweighted total variationexistence and uniqueness of weak solutionVlasov-McKean equations

Mathematics Subject Classification ID

Lyapunov and storage functions (93D30) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) Vlasov equations (35Q83)

Related Items (12)

Distribution dependent SDEs driven by additive continuous noise ⋮ Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion ⋮ Approximations of McKean-Vlasov stochastic differential equations with irregular coefficients ⋮ Rate of homogenization for fully-coupled McKean–Vlasov SDEs ⋮ Uniqueness for nonlinear Fokker-Planck equations and for McKean-Vlasov SDEs: the degenerate case ⋮ Mean-field stochastic differential equations with a discontinuous diffusion coefficient ⋮ Stochastic averaging principle for two-time-scale SPDEs driven by fractional Brownian motion with distribution dependent coefficients ⋮ Distribution-dependent SDEs with Hölder continuous drift and \(\alpha\)-stable noise ⋮ On Pathwise Uniqueness of Solutions for Multidimensional McKean--Vlasov Equation ⋮ On convergence to stationary distributions for solutions of nonlinear Fokker-Planck-Kolmogorov equations ⋮ Weak existence and uniqueness for McKean-Vlasov SDEs with common noise ⋮ Stochastic averaging principle for distribution dependent stochastic differential equations

Cites Work

• Unnamed Item
• On uniqueness of solutions to nonlinear Fokker-Planck-Kolmogorov equations
• On a strong form of propagation of chaos for McKean-Vlasov equations
• Distribution dependent SDEs for Landau type equations
• Strong solutions of mean-field stochastic differential equations with irregular drift
• Distribution dependent SDEs with singular coefficients
• McKean-Vlasov SDEs under measure dependent Lyapunov conditions
• Freidlin-Wentzell LDP in path space for McKean-Vlasov equations and the functional iterated logarithm law
• Nonlinear Fokker-Planck equations for probability measures on path space and path-distribution dependent sdes
• Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations
• Existence and uniqueness theorems for solutions of McKean–Vlasov stochastic equations

This page was built for publication: Weak solutions to Vlasov–McKean equations under Lyapunov-type conditions