Multiparameter L\'evy white noise theory and applications
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt {\O}ksendal
TL;DR
This paper develops a comprehensive white noise theory for multi-parameter Lévy sheets and their Poisson measures, enabling advanced analysis of stochastic PDEs driven by Lévy noise.
Contribution
It introduces a novel white noise calculus framework for multi-parameter Lévy processes, extending existing theories to more complex stochastic systems.
Findings
Established a white noise calculus for Lévy sheets.
Applied the theory to stochastic PDEs with Lévy noise.
Provided mathematical tools for analyzing Lévy-driven stochastic systems.
Abstract
We construct a white noise theory and white noise calculus for the (multi-parameter) L\' evy sheet and its compensated Poisson random measures. The theory applies to stochastic partial differential equations subject to L\' evy noise.
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