Gaussian approximation of multivariate Lévy processes with applications to simulation of tempered stable processes

Abstract

The problem of simulation of multivariate Lévy processes is investigated. A method based on generalized shot noise series representations of Lévy processes combined with Gaussian approximation of the remainder is established in full generality. This method is applied to multivariate stable and tempered stable processes and formulae for their approximate simulation are obtained. © 2007 ISI/BS.