Open AccessItô Formula for Integral Processes Related to Space-Time Lévy Noise
Author(s) -
Raluca M. Balan,
Cheikh B. Ndongo
Publication year - 2015
Publication title -
applied mathematics
Language(s) - English
Resource type - Journals
eISSN - 2152-7393
pISSN - 2152-7385
DOI - 10.4236/am.2015.610156
Subject(s) - mathematics , white noise , gaussian noise , noise (video) , mathematical analysis , space time , representation (politics) , moment (physics) , additive white gaussian noise , second moment of area , space (punctuation) , gaussian , mathematical physics , physics , computer science , classical mechanics , quantum mechanics , statistics , geometry , law , chemical engineering , politics , political science , engineering , image (mathematics) , operating system , algorithm , artificial intelligence
In this article, we give a new proof of the Ito formula for some integral processes related to the space-time Levy 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 Levy noise with finite variance: a maximal inequality for the p-th moment of the stochastic integral, and the Ito representation theorem leading to a chaos expansion similar to the Gaussian case.
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