{"paper":{"title":"Tail Behavior of Randomly Weighted Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Krishanu Maulik, Rajat Subhra Hazra","submitted_at":"2010-11-19T06:10:46Z","abstract_excerpt":"Let $\\{X_t, t \\geq 1\\}$ be a sequence of identically distributed and pairwise asymptotically independent random variables with regularly varying tails and $\\{ \\Theta_t, t\\geq1 \\}$ be a sequence of positive random variables independent of the sequence $\\{X_t, t \\geq 1\\}$. We shall discuss the tail probabilities and almost sure convergence of $\\xinf=\\sum_{t=1}^{\\infty}\\Theta_t X_t^{+}$ (where $X^+=\\max\\{0,X\\}$) and $\\max_{1\\leq k<\\infty} \\sum_{t=1}^{k}\\Theta_t X_t$ and provide some sufficient conditions motivated by Denisov and Zwart (2007) as alternatives to the usual moment conditions. In part"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4349","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"}