L\'evy Processes, Generalized Moments and Uniform Integrability
Probability
2022-02-21 v2
Abstract
We give new proofs of certain equivalent conditions for the existence of generalized moments of a L\'evy process ; in particular, the existence of a generalized -moment is equivalent to the uniform integrability of . As a consequence, certain functions of a L\'evy process which are integrable and local martingales are already true martingales. Our methods extend to moments of stochastically continuous additive processes, and we give new, short proofs for the characterization of lattice distributions and the transience of L\'evy processes.
Cite
@article{arxiv.2102.09004,
title = {L\'evy Processes, Generalized Moments and Uniform Integrability},
author = {David Berger and Franziska Kühn and René L. Schilling},
journal= {arXiv preprint arXiv:2102.09004},
year = {2022}
}