English

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}
}