{"paper":{"title":"Correlated Poisson processes and self-decomposable laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","q-fin.CP"],"primary_cat":"math.PR","authors_text":"Nicola Cufaro Petroni, Piergiacomo Sabino","submitted_at":"2015-09-02T10:21:13Z","abstract_excerpt":"We analyze a method to produce pairs of non independent Poisson processes $M(t),N(t)$ from positively correlated, self-decomposable, exponential renewals. In particular the present paper provides the family of copulas pairing the renewals, along with the closed form for the joint distribution $p_{m,n}(s,t)$ of the pair $\\big(M(s),N(t)\\big)$, an outcome which turns out to be instrumental to produce explicit algorithms for applications in finance and queuing theory. We finally discuss the cross-correlation properties of the two processes and the relative timing of their jumps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00629","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"}