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

2018/01/11 by Linghua Chen, Espen R. Jakobsen, Chen, Linghua +1
Economics, Econometrics and Finance · Mathematics · #35K10 #47D06 #47D07 #47G20 #60G51 #60H10 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1801.03914

openalex publication_date 2018/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a new generation result in L¹ 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.

Citations

• Transition Probabilities for Symmetric Jump Processes

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