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arXiv · 1211.2973

Itô calculus and jump diffusions for $G$-Lévy processes

Krzysztof Paczka
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Abstract

The paper considers the integration theory for $G$-Lévy processes with finite activity. We introduce the Itô-Lévy integrals, give the Itô formula for them and establish SDE's, BSDE's and decoupled FBSDE's driven by $G$-Lévy processes. In order to develop such a theory, we prove two key results: the representation of the sublinear expectation associated with a $G$-Lévy process and a characterization of random variables in $L^p_G(Ω)$ in terms of their quasi-continuity.

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Krzysztof Paczka. 2014-11-10. Itô calculus and jump diffusions for $G$-Lévy processes. https://arxiv.org/abs/1211.2973

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