A generalised It\=o formula for L\'evy-driven Volterra processes
Probability
2015-03-03 v3
Abstract
We derive a generalised It\=o formula for stochastic processes which are constructed by a convolution of a deterministic kernel with a centred L\'evy process. This formula has a unifying character in the sense that it contains the classical It\=o formula for L\'evy 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 L\'evy processes (with Mandelbrot-Van Ness kernel) and a wide class of related processes for which such a generalised It\=o formula has not yet been available in the literature.
Cite
@article{arxiv.1402.6568,
title = {A generalised It\=o formula for L\'evy-driven Volterra processes},
author = {Christian Bender and Robert Knobloch and Philip Oberacker},
journal= {arXiv preprint arXiv:1402.6568},
year = {2015}
}
Comments
Stochastic Processes and their Applications (2015), http://dx.doi.org/10.1016/j.spa.2015.02.009