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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AM> Vol.6 No.10, September 2015

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

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DOI: 10.4236/am.2015.610156 2,593 Downloads 3,000 Views Citations

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Raluca M. Balan^*, Cheikh B. Ndongo

Affiliation(s)

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

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.

Cite this paper

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.

References

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