One dimensional critical kinetic Fokker-Planck equations, Bessel and stable processes

DOI10.1007/s00220-020-03903-0zbMath1457.35085arXiv1805.09728OpenAlexW3120372422MaRDI QIDQ2223723

Nicolas Fournier, Camille Tardif

Publication date: 1 February 2021

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.09728

zbMATH Keywords

Bessel processBrownian motionkinetic Fokker-Planck equations

Mathematics Subject Classification ID

Brownian motion (60J65) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Fokker-Planck equations (35Q84)

Related Items

Scaling limit of a kinetic inhomogeneous stochastic system in the quadratic potential ⋮ Fractional diffusion for Fokker–Planck equation with heavy tail equilibrium: An à la Koch spectral method in any dimension ⋮ Stable limit theorems for additive functionals of one-dimensional diffusion processes ⋮ Classical and quantum mechanical models of many-particle systems. Abstracts from the workshop held November 29 -- December 5, 2020 (online meeting) ⋮ Fractional hypocoercivity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fractional diffusion limit for collisional kinetic equations: a Hilbert expansion approach
• Fractional diffusion limit for collisional kinetic equations
• Limit theorems for additive functionals of a Markov chain
• Diffusion approximation for Fokker Planck with heavy tail equilibria: a spectral method in dimension 1
• On the Poisson equation and diffusion approximation. I
• Anomalous diffusion for multi-dimensional critical kinetic Fokker-Planck equations
• Diffusion limit for kinetic Fokker-Planck equation with heavy tails equilibria: the critical case
• Central limit theorems for additive functionals of ergodic Markov diffusions processes
• ANOMALOUS DIFFUSION LIMIT FOR KINETIC EQUATIONS WITH DEGENERATE COLLISION FREQUENCY
• Fractional diffusion limit for collisional kinetic equations: A moments method
• On constants related to the choice of the local time at 0, and the corresponding Itô measure for Bessel processes with dimension d = 2(1 − α ), 0 < α < 1
• Diffusion limit of Fokker−Planck equation with heavy tail equilibria