Existence of periodic probability solutions to Fokker-Planck equations with applications

DOI10.1016/j.jfa.2019.108281zbMath1428.35600OpenAlexW2964986932WikidataQ127433833 ScholiaQ127433833MaRDI QIDQ2326495

Yanyan Li

Publication date: 7 October 2019

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2019.108281

zbMATH Keywords

Fokker-Planck equationstochastic differential inclusionperiodic probability solutionstochastic damping Hamiltonian system

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stability of topological dynamical systems (37B25) Diffusion processes (60J60) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Fokker-Planck equations (35Q84)

Related Items (22)

LaSalle-type stationary oscillation principle for stochastic affine periodic systems ⋮ Periodic measure of a stochastic non-autonomous predator-prey system with impulsive effects ⋮ Periodic solutions of stochastic functional differential equations with jumps via viability ⋮ Poisson stable solutions for stochastic functional evolution equations with infinite delay ⋮ Periodic measures for a class of SPDEs with regime-switching ⋮ Recent Results on Recurrent Solutions and Limit Distributions of SDEs ⋮ Cuplength estimates for time-periodic measures of Hamiltonian systems with diffusion ⋮ Towards mesoscopic ergodic theory ⋮ Persistence and periodic measure of a stochastic predator–prey model with Beddington–DeAngelis functional response ⋮ Existence of periodic solutions in distribution for stochastic Newtonian systems ⋮ Unnamed Item ⋮ Periodic solutions for SDEs through upper and lower solutions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Periodic, almost periodic and almost automorphic solutions for SPDEs with monotone coefficients ⋮ Periodic solution of stochastic process in the distributional sense ⋮ Convergence to Periodic Probability Solutions in Fokker--Planck Equations ⋮ Poisson stable solutions for stochastic differential equations with Lévy noise ⋮ Periodic averaging principle for neutral stochastic delay differential equations with impulses ⋮ Periodic solutions in distribution of stochastic lattice differential equations ⋮ Periodic solutions in distribution of mean-field stochastic differential equations ⋮ Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Steady states of Fokker-Planck equations. I: Existence
• On the Cauchy problem for Fokker-Planck-Kolmogorov equations with potential terms on arbitrary domains
• Periodic solutions of Fokker-Planck equations
• Pathwise random periodic solutions of stochastic differential equations
• Some properties of set-valued stochastic integrals
• Stochastic flows of SDEs with irregular coefficients and stochastic transport equations
• Stochastic differential equations with coefficients in Sobolev spaces
• Random periodic solutions of random dynamical systems
• On positive and probability solutions to the stationary Fokker-Planck-Kolmogorov equation
• Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems.
• Stability of regime-switching stochastic differential equations
• Stochastic differential inclusions and applications.
• On uniqueness problems related to elliptic equations for measures
• Periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent and Poisson stable solutions for stochastic differential equations
• On uniqueness problems related to the Fokker-Planck-Kolmogorov equation for measures
• Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients
• Is Lebesgue measure the only \(\sigma\)-finite invariant Borel measure?
• ON REGULARITY OF TRANSITION PROBABILITIES AND INVARIANT MEASURES OF SINGULAR DIFFUSIONS UNDER MINIMAL CONDITIONS
• Ergodic Control of Diffusion Processes
• Fokker–Planck–Kolmogorov Equations
• Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients
• Elliptic and parabolic equations for measures
• Markov Chains and Stochastic Stability
• Periodic solutions of affine stochastic differential equations
• A Generalization of Khasminskii's Theorem on the Existence of Invariant Measures for Locally Integrable Drifts
• Uniqueness of solutions of elliptic equations and uniqueness of invariant measures of diffusions
• An Introduction to the Theory of Point Processes
• Ergodicity for Infinite Dimensional Systems
• An overlook on statistical inference issues for stochastic damping hamiltonian systems under the fluctuation-dissipation condition
• Ergodic Properties of Markov Processes
• On Parabolic Equations for Measures
• Riemannian geometry and geometric analysis

This page was built for publication: Existence of periodic probability solutions to Fokker-Planck equations with applications