arXiv:1505.04685v1 [math.PR] 18 May 2015 Itˆ o formula for integral processes related to space-time L´ evy white noise Raluca M. Balan ∗† Cheikh B. Ndongo ‡ May 18, 2015 Abstract In this article, we give a new proof of the Itˆo formula for some integral processes related to the space-time L´ evy noise introduced in [2] and [3] 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 L´ evy noise with finite variance: a maximal inequality for the p-th moment of the stochastic integral, and the Itˆo representation theorem leading to a chaos expansion similar to the Gaussian case. Keywords: L´ evy processes, Poisson random measure, stochastic integral, Itˆo formula, Itˆo representation theorem MSC 2010 subject classification: Primary 60H05; secondary 60G51 * Corresponding author. University of Ottawa, Department of Mathematics and Statis- tics, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada. E-mail address: rbalan@uottawa.ca † Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada. ‡ University of Ottawa, Department of Mathematics and Statistics, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada. E-mail address: cndon072@uottawa.ca 1