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Itô Formula for Integral Processes Related to Space-Time Lévy Noise
Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada
Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada
- 1 Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada
- 2 Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada
Applied Mathematics·Volume 06 (2015)·Pages 1755–1768·Published 8 September 2015·DOI10.4236/am.2015.610156
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Abstract
In this article, we give a new proof of the It ô 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 It ô representation theorem leading to a chaos expansion similar to the Gaussian case.
KeywordsL&eacutevy ProcessesPoisson Random MeasureStochastic IntegralIt&OcircFormulaIt&OcircRepresentation Theorem
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