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arXiv · 1801.03914

$L^1$ semigroup generation for Fokker-Planck operators associated with general L\'evy driven SDEs

Linghua Chen·Espen Robstad Jakobsen
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Abstract

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 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.

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Linghua Chen, Espen Robstad Jakobsen. 2018-01-11. $L^1$ semigroup generation for Fokker-Planck operators associated with general L\'evy driven SDEs. https://arxiv.org/abs/1801.03914

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