%0 Journal Article
%T Maximal inequalities for fractional L¨¦vy and related processes
%A Christian Bender
%A Robert Knobloch
%A Philip Oberacker
%J Mathematics
%D 2014
%I arXiv
%X 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 $p$-integrable and we derive maximal inequalities in terms of the kernel and of the moments of the driving martingale.
%U http://arxiv.org/abs/1408.1257v1