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

Raluca M. Balan; Cheikh B. Ndongo

doi:10.4236/am.2015.610156

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Applied Mathematics > Vol.6 No.10, September 2015

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 PDF HTML XML 2,732 Downloads 3,152 Views Citations

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

Share and Cite:

Balan, R. and Ndongo, C. (2015) Itô Formula for Integral Processes Related to Space-Time Lévy Noise. Applied Mathematics, 6, 1755-1768. doi: 10.4236/am.2015.610156.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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