Markov property of monotone L\'evy processes
Probability
2021-04-21 v1
Abstract
Monotone L\'evy processes with additive increments are defined and studied. It is shown that these processes have a natural Markov structure and their Markov transition semigroups are characterized using the monotone L\'evy-Khintchine formula. Monotone L\'evy processes turn out to be related to classical L\'evy processes via Attal's ``remarkable transformation.'' A monotone analogue of the family of exponential martingales associated to a classical L\'evy process is also defined.
Cite
@article{arxiv.math/0401390,
title = {Markov property of monotone L\'evy processes},
author = {Uwe Franz and Naofumi Muraki},
journal= {arXiv preprint arXiv:math/0401390},
year = {2021}
}
Comments
21 pages