Local Malliavin Calculus for L\'evy Processes and Applications
Probability
2012-10-04 v1
Abstract
In this paper a Malliavin calculus for L\'evy processes based on a family of true derivative operators is developed. The starting point is an extension to L\'evy processes of the pioneering paper by Carlen and Pardoux [8] for the Poisson process, and our approach includes also the classical Malliavin derivative for Gaussian processes. We obtain a sufficient condition for the absolute continuity of functionals of the L\'evy process. As an application, we analyze the absolute continuity of the law of the solution of some stochastic differential equations.
Keywords
Cite
@article{arxiv.1210.1156,
title = {Local Malliavin Calculus for L\'evy Processes and Applications},
author = {Jorge A. León and Josep L. Solé and Frederic Utzet and Josep Vives},
journal= {arXiv preprint arXiv:1210.1156},
year = {2012}
}