Itô Formula for Integral Processes Related to Space-Time Lévy Noise

Raluca M. Balan^*, Cheikh B. Ndongo

Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada.

DOI: 10.4236/am.2015.610156                

Abstract

In this article, we give a new proof of the Itô formula for some integral processes related to the space-time Lévy noise introduced in [1] [2] 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.

Keywords

Lévy Processes, Poisson Random Measure, Stochastic Integral, ItÔ Formula, ItÔ Representation Theorem

Conflicts of Interest

The authors declare no conflicts of interest.

References

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