Maximal inequalities for fractional Lévy and related processes

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 Lévy process, which covers the popular class of fractional Lévy 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.

References in corpus (2)

• Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes
• Stochastic calculus for convoluted Lévy processes

Cited by in corpus (2)

• A generalised Itō formula for Lévy-driven Volterra processes
• On the conditional small ball property of multivariate Lévy-driven moving average processes