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arXiv · 1408.1257

Maximal inequalities for fractional L\'evy and related processes

Christian Bender·Robert Knobloch·Philip Oberacker
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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 $p$-integrable and we derive maximal inequalities in terms of the kernel and of the moments of the driving martingale.

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Christian Bender, Robert Knobloch, Philip Oberacker. 2014-08-06. Maximal inequalities for fractional L\'evy and related processes. https://doi.org/10.1080/07362994.2015.1036167

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