Table of Contents
International Journal of Stochastic Analysis
Volume 2017, Article ID 9693153, 9 pages
https://doi.org/10.1155/2017/9693153
Research Article

Malliavin Differentiability of Solutions of SPDEs with Lévy White Noise

Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON, Canada K1N 6N5

Correspondence should be addressed to Raluca M. Balan; ac.awattou@nalabr

Received 2 January 2017; Accepted 21 February 2017; Published 12 March 2017

Academic Editor: Bohdan Maslowski

Copyright © 2017 Raluca M. Balan and Cheikh B. Ndongo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a stochastic partial differential equation (SPDE) driven by a Lévy white noise, with Lipschitz multiplicative term . We prove that, under some conditions, this equation has a unique random field solution. These conditions are verified by the stochastic heat and wave equations. We introduce the basic elements of Malliavin calculus with respect to the compensated Poisson random measure associated with the Lévy white noise. If is affine, we prove that the solution is Malliavin differentiable and its Malliavin derivative satisfies a stochastic integral equation.