{"paper":{"title":"The product of dependent random variables with applications to a discrete-time risk model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fengyang Cheng, Hui Xu, Jikun Chen","submitted_at":"2016-06-12T01:33:09Z","abstract_excerpt":"Let $X$ be a real valued random variable with an unbounded distribution $F$ and let $Y$ be a nonnegative valued random variable with a unbounded distribution $G$, which satisfy that\n  \\begin{eqnarray*} P(X>x|Y=y)\\sim h(y)P(X>x) \\end{eqnarray*} holds uniformly for $y\\geq0$ as $x\\to \\infty$. Under the condition that $\\overline{G}(bx)=o(\\overline H(x))$ holds for all constant $b>0$, we proved that $F\\in\\mathcal{L}(\\gamma)$ for some $\\gamma\\geq 0$ implied $H\\in \\mathcal{L}(\\gamma/\\beta_G)$ and that $F\\in\\mathcal{S}(\\gamma)$ for some $\\gamma\\geq 0$ implied $H\\in \\mathcal{S}(\\gamma/\\beta_G)$, where "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03651","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"}