{"paper":{"title":"It\\^o calculus and jump diffusions for $G$-L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Krzysztof Paczka","submitted_at":"2012-11-13T12:46:41Z","abstract_excerpt":"The paper considers the integration theory for $G$-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 $G$-L\\'evy processes. In order to develop such a theory, we prove two key results: the representation of the sublinear expectation associated with a $G$-L\\'evy process and a characterization of random variables in $L^p_G(\\Omega)$ in terms of their quasi-continuity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2973","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}