Maximal inequalities for fractional L\'evy and related processes
Probability
2021-05-31 v1
Abstract
In this paper we study processes which are constructed by a convolution of a deterministic kernel with a martingale. A special emphasis is put on the case where the driving martingale is a centred L\'evy process, which covers the popular class of fractional L\'evy processes. As a main result we show that, under appropriate assumptions on the kernel and the martingale, the maximum process of the corresponding `convoluted martingale' is -integrable and we derive maximal inequalities in terms of the kernel and of the moments of the driving martingale.
Keywords
Cite
@article{arxiv.1408.1257,
title = {Maximal inequalities for fractional L\'evy and related processes},
author = {Christian Bender and Robert Knobloch and Philip Oberacker},
journal= {arXiv preprint arXiv:1408.1257},
year = {2021}
}