L1 semigroup generation for Fokker-Planck operators associated with general Levy driven SDEs
Journal article, Peer reviewed
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OriginalversjonDiscrete and Continuous Dynamical Systems. Series A. 2018, 38 (11), 5735-5763. 10.3934/dcds.2018250
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.