{"paper":{"title":"Inversions of infinitely divisible distributions and conjugates of stochastic integral mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ken-iti Sato","submitted_at":"2012-04-09T11:50:24Z","abstract_excerpt":"The dual of an infinitely divisible distribution on $\\mathbb{R}^d$ without Gaussian part defined in Sato, ALEA {\\bf 3} (2007), 67--110, is renamed to the inversion. Properties and characterization of the inversion are given. A stochastic integral mapping is a mapping $\\mu=\\Phi_{f}\\rho$ of $\\rho$ to $\\mu$ in the class of infinitely divisible distributions on $\\mathbb{R}^d$, where $\\mu$ is the distribution of an improper stochastic integral of a nonrandom function $f$ with respect to a L\\'{e}vy process on $\\mathbb{R}^d$ with distribution $\\rho$ at time 1. The concept of the conjugate is introduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1861","kind":"arxiv","version":1},"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"}