American Institute of Mathematical Sciences

November  2018, 38(11): 5735-5763. doi: 10.3934/dcds.2018250

L1 semigroup generation for Fokker-Planck operators associated to general Lévy driven SDEs

 Norwegian University of Science and Technology, NO-7491, Trondheim, Norway

* Corresponding author: Espen R. Jakobsen

Received  January 2018 Revised  June 2018 Published  August 2018

Fund Project: E. R. Jakobsen is supported by the Toppforsk (research excellence) project Waves and Nonlinear Phenomena (WaNP), grant no. 250070 from the Research Council of Norway

We prove a new generation result in $L^1$ 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 Lévy 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 Lévy operators, including state-space depending coefficients with linear growth and general Lévy measures which can be singular and have fat tails.

Citation: Linghua Chen, Espen R. Jakobsen. L1 semigroup generation for Fokker-Planck operators associated to general Lévy driven SDEs. Discrete & Continuous Dynamical Systems - A, 2018, 38 (11) : 5735-5763. doi: 10.3934/dcds.2018250
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