Diffusion approximation for Fokker Planck with heavy tail equilibria : a spectral method in dimension 1
Analysis of PDEs
2017-11-09 v1
Abstract
This paper is devoted to the diffusion approximation for the 1-d Fokker Planck equation with a heavy tail equilibria of the form (1+v^2)^{-\beta/2}, in the range beta\in ]1,5[. We prove that the limit diffusion equation involves a fractional Laplacian kappa|\Delta|^{\frac{\beta+1}{6}}, and we compute the value of the diffusion coefficient kappa. This extends previous results of E. Nasreddine and M. Puel in the case beta>5, and of P. Cattiaux, E. Nasreddine and M. Puel in the case beta=5.
Keywords
Cite
@article{arxiv.1711.03060,
title = {Diffusion approximation for Fokker Planck with heavy tail equilibria : a spectral method in dimension 1},
author = {Gilles Lebeau and Marjolaine Puel},
journal= {arXiv preprint arXiv:1711.03060},
year = {2017}
}