{"paper":{"title":"A random integral calculus on generalized s-selfdecomposable probability measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Zbigniew J. Jurek","submitted_at":"2010-10-01T11:59:35Z","abstract_excerpt":"It is known that the class $\\mathcal{U}_{\\beta}$, of generalized s-selfdecom-posable probability distributions, can be viewed as an image via random integral mapping $\\mathcal{J}^{\\beta}$ of the class $ID$ of all infinitely divisible measures. We prove that a composition of the mappings $\\mathcal{J}^{\\beta_1}, \\mathcal{J}^{\\beta_2}, ..., \\mathcal{J}^{\\beta_n}$ is again random integral mapping but with a new inner time. In a proof some form of Lagrange interpolation formula is needed. Moreover, some elementary formulas concerning the distributions of products of powers of independent uniformly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0131","kind":"arxiv","version":2},"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"}