On the Liouville property for non-local Lévy generators

2019/09/03 by Victoria Knopova, Knopova, Victoria, René L. Schilling +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1909.01237

openalex publication_date 2019/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a necessary and sufficient condition for the Liouville property of the infinitesimal generator of a Lévy process and subordinate Lévy processes. Combining our criterion with the necessary and sufficient condition obtained by Alibaud et al., we obtain a characterization of (orthogonal subgroup of the) the set of zeros of the characteristic exponent of the Lévy process.

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