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arXiv · 1402.6568

A generalised Itō formula for Lévy-driven Volterra processes

Christian Bender·Robert Knobloch·Philip Oberacker
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Abstract

We derive a generalised Itō formula for stochastic processes which are constructed by a convolution of a deterministic kernel with a centred Lévy process. This formula has a unifying character in the sense that it contains the classical Itō formula for Lévy processes as well as recent change-of-variable formulas for Gaussian processes such as fractional Brownian motion as special cases. Our result also covers fractional Lévy processes (with Mandelbrot-Van Ness kernel) and a wide class of related processes for which such a generalised Itō formula has not yet been available in the literature.

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BibTeXRIS

Christian Bender, Robert Knobloch, Philip Oberacker. 2015-03-02. A generalised Itō formula for Lévy-driven Volterra processes. https://doi.org/10.1016/j.spa.2015.02.009

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