$L^1$ semigroup generation for Fokker-Planck operators associated with general L\'evy driven SDEs
Dynamical Systems
2018-01-12 v1
Abstract
We prove a new generation result in for a large class of non-local operators with non-degenerate local terms. This class contains the operators appearing in Fokker-Planck or Kolmogorov forward equations associated with L\'evy driven SDEs, i.e. the adjoint operators of the infinitesimal generators of these SDEs. As a byproduct, we also obtain a new elliptic regularity result of independent interest. The main novelty in this paper is that we can consider very general L\'evy operators, including state-space depending coefficients with linear growth and general L\'evy measures which can be singular and have fat tails.
Keywords
Cite
@article{arxiv.1801.03914,
title = {$L^1$ semigroup generation for Fokker-Planck operators associated with general L\'evy driven SDEs},
author = {Linghua Chen and Espen Robstad Jakobsen},
journal= {arXiv preprint arXiv:1801.03914},
year = {2018}
}