Itô formula for integral processes related to space-time Lévy white noise

Abstract

In this article, we give a new proof of the Itô formula for some integral processes related to the space-time Lévy white noise introduced in Balan (2015) as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two applications of this result, which are useful in the study of SPDEs driven by a space-time Lévy noise with finite variance: a maximal inequality for the $p$-th moment of the stochastic integral, and the Itô representation theorem leading to a chaos expansion similar to the Gaussian case.

21 pages