On two multistable extensions of stable L\'evy motion and their semimartingale representation
Probability
2013-10-25 v2
Abstract
We compare two definitions of multistable L\'evy motions. Such processes are extensions of classical L\'evy motion where the stability index is allowed to vary in time. We show that the two multistable L\'evy motions have distinct properties: in particular, one is a pure-jump Markov process, while the other one satisfies neither of these properties. We prove that both are semimartingales and provide semimartingale decompositions.
Keywords
Cite
@article{arxiv.1209.2236,
title = {On two multistable extensions of stable L\'evy motion and their semimartingale representation},
author = {Ronan Le Guével and Jacques Lévy-Vehel and Lining Liu},
journal= {arXiv preprint arXiv:1209.2236},
year = {2013}
}
Comments
Accepted for publication in Journal of Theoretical Probability