{"paper":{"title":"A class of multivariate infinitely divisible distributions related to arcsine density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Ken-iti Sato, Makoto Maejima, V\\'ictor P\\'erez-Abreu","submitted_at":"2012-05-08T10:14:49Z","abstract_excerpt":"Two transformations $\\mathcal{A}_1$ and $\\mathcal{A}_2$ of L\\'{e}vy measures on $\\mathbb{R}^d$ based on the arcsine density are studied and their relation to general Upsilon transformations is considered. The domains of definition of $\\mathcal{A}_1$ and $\\mathcal{A}_2$ are determined and it is shown that they have the same range. The class of infinitely divisible distributions on $\\mathbb{R}^d$ with L\\'{e}vy measures being in the common range is called the class $A$ and any distribution in the class $A$ is expressed as the law of a stochastic integral $\\int_0^1\\cos(2^{-1}\\uppi t)\\,\\mathrm{d}X_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1654","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"}