A generalised Itō formula for Lévy-driven Volterra processes

Christian Bender, Robert Knobloch and Philip Oberacker

Stochastic Processes and their Applications, 2015, vol. 125, issue 8, 2989-3022

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.

Keywords: Fractional Lévy process; Itō formula; Skorokhod integral; Stochastic convolution; S-transform (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:8:p:2989-3022

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DOI: 10.1016/j.spa.2015.02.009

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