On the Liouville property for non-local L\'evy generators
Probability
2019-09-04 v1 Analysis of PDEs
Abstract
We prove a necessary and sufficient condition for the Liouville property of the infinitesimal generator of a L\'evy process and subordinate L\'evy 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 L\'evy process.
Keywords
Cite
@article{arxiv.1909.01237,
title = {On the Liouville property for non-local L\'evy generators},
author = {Victoria Knopova and René Schilling},
journal= {arXiv preprint arXiv:1909.01237},
year = {2019}
}