Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures
From MaRDI portal
Publication:1740616
DOI10.1016/j.jfa.2019.03.014zbMath1411.60010arXiv1801.02446OpenAlexW2963503063MaRDI QIDQ1740616
Michael Roeckner, Vladimir I. Bogachev, Stanislav V. Shaposhnikov
Publication date: 2 May 2019
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1801.02446
Convergence of probability measures (60B10) Initial value problems for second-order parabolic equations (35K15) Stable stochastic processes (60G52) Transition functions, generators and resolvents (60J35) Integro-differential operators (47G20) PDEs with measure (35R06)
Related Items (11)
Zvonkin’s transform and the regularity of solutions to double divergence form elliptic equations ⋮ Vladimir Igorevich Bogachev ⋮ Existence, uniqueness and exponential ergodicity under Lyapunov conditions for McKean-Vlasov SDEs with Markovian switching ⋮ The evolution to equilibrium of solutions to nonlinear Fokker-Planck equation ⋮ Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes ⋮ Non-uniform Kozlov–Treschev averagings in the ergodic theorem ⋮ On convergence to stationary distributions for solutions of nonlinear Fokker-Planck-Kolmogorov equations ⋮ McKean-Vlasov SDEs under measure dependent Lyapunov conditions ⋮ Differential properties of semigroups and estimates of distances between stationary distributions of diffusions ⋮ Mean-field Langevin dynamics and energy landscape of neural networks ⋮ Periodic solutions in distribution of mean-field stochastic differential equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Reflection couplings and contraction rates for diffusions
- Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
- Nonlinear elliptic equations for measures
- Contractions in the 2-Wasserstein length space and thermalization of granular media
- On uniqueness of solutions to nonlinear Fokker-Planck-Kolmogorov equations
- Phi-entropy inequalities for diffusion semigroups
- Non-uniqueness of stationary measures for self-stabilizing processes
- Coupling methods for multidimensional diffusion processes
- On invariant measures of nonlinear Markov processes
- Harnack and functional inequalities for generalized Mehler semigroups.
- Distribution dependent SDEs for Landau type equations
- Nonlinear Fokker-Planck-Kolmogorov equations for measures
- Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations
- Nonlinear self-stabilizing processes. I: Existence, invariant probability, propagation of chaos
- Nonlinear self-stabilizing processes. II: Convergence to invariant probability
- Exponential and uniform ergodicity of Markov processes
- The Kantorovich and variation distances between invariant measures of diffusions and nonlinear stationary Fokker-Planck-Kolmogorov equations
- Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré
- Nonlinear Fokker-Planck equations. Fundamentals and applications.
- Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations
- ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
- Exponential convergence in Lp-Wasserstein distance for diffusion processes without uniformly dissipative drift
- Yet Another Look at Harris’ Ergodic Theorem for Markov Chains
- A certain class of diffusion processes associated with nonlinear parabolic equations
- Long time behavior of Markov processes
- Fokker–Planck–Kolmogorov Equations
- Large deviations, free energy functional and quasi-potential for a mean field model of interacting diffusions
- Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes
- Distances between Stationary Distributions of Diffusions and Solvability of Nonlinear Fokker--Planck--Kolmogorov Equations
- On Ergodic Properties of Nonlinear Markov Chains and Stochastic McKean--Vlasov Equations
- Nonlinear parabolic equations for measures
- A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS
This page was built for publication: Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures
