{"paper":{"title":"Functionals of a L\\'evy Process on Canonical and Generic Probability Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Steinicke","submitted_at":"2013-04-23T15:31:49Z","abstract_excerpt":"We develop an approach to Malliavin calculus for L\\'evy processes from the perspective of expressing a random variable $Y$ by a functional $F$ mapping from the Skorohod space of c\\`adl\\`ag functions to $\\mathbb{R}$, such that $Y=F(X)$ where $X$ denotes the L\\'evy process. We also present a chain-rule-type application for random variables of the form $f(\\omega,Y(\\omega))$.\n  An important tool for these results is a technique which allows us to transfer identities proved on the canonical probability space (in the sense of Sol\\'e et al.) associated to a L\\'evy process with triplet $(\\gamma,\\sigma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6324","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"}