It\^o calculus and jump diffusions for $G$-L\'evy processes
Probability
2014-11-11 v3
Abstract
The paper considers the integration theory for -L\'evy processes with finite activity. We introduce the It\^o-L\'evy integrals, give the It\^o formula for them and establish SDE's, BSDE's and decoupled FBSDE's driven by -L\'evy processes. In order to develop such a theory, we prove two key results: the representation of the sublinear expectation associated with a -L\'evy process and a characterization of random variables in in terms of their quasi-continuity.
Keywords
Cite
@article{arxiv.1211.2973,
title = {It\^o calculus and jump diffusions for $G$-L\'evy processes},
author = {Krzysztof Paczka},
journal= {arXiv preprint arXiv:1211.2973},
year = {2014}
}