{"paper":{"title":"Description of limits of ranges of iterations of stochastic integral mappings of infinitely divisible distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ken-iti Sato","submitted_at":"2010-12-01T04:45:31Z","abstract_excerpt":"For infinitely divisible distributions $\\rho$ on $\\mathbb{R}^d$ the stochastic integral mapping $\\Phi_f\\rho$ is defined as the distribution of improper stochastic integral $\\int_0^{\\infty-} f(s) dX_s^{(\\rho)}$, where $f(s)$ is a non-random function and $\\{X_s^{(\\rho)}\\}$ is a L\\'evy process on $\\mathbb{R}^d$ with distribution $\\rho$ at time 1. For three families of functions $f$ with parameters, the limits of the nested sequences of the ranges of the iterations $\\Phi_f^n$ are shown to be some subclasses, with explicit description, of the class $L_{\\infty}$ of completely selfdecomposable distri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0093","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"}