{"paper":{"title":"A calculus on L\\'evy exponents and selfdecomposability on Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Zbigniew J. Jurek","submitted_at":"2008-11-23T15:32:52Z","abstract_excerpt":"In infinite dimensional Banach spaces there is no complete characterization of the L\\'evy exponents of infinitely divisible probability measures. Here we propose \\emph{a calculus on L\\'evy exponents} that is derived from some random integrals. As a consequence we prove that \\emph{each} selfdecomposable measure can by factorized as another selfdecomposable measure and its background driving measure that is s-selfdecomposable. This complements a result from the paper of Iksanov-Jurek-Schreiber in the Annals of Probability \\textbf{32}, 2004.}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.3752","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"}