{"paper":{"title":"Asymptotics for Weighted Random Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mariana Olvera-Cravioto","submitted_at":"2011-02-01T21:28:20Z","abstract_excerpt":"Let $\\{X_i\\}$ be a sequence of independent identically distributed random variables with an intermediate regularly varying (IR) right tail $\\bar{F}$. Let $(N, C_1, ..., C_N)$ be a nonnegative random vector independent of the $\\{X_i\\}$ with $N \\in \\mathbb{N} \\cup \\{\\infty\\}$. We study the weighted random sum $S_N = \\sum_{i=1}^N C_i X_i$, and its maximum, $M_N = \\sup_{1 \\leq k < N+1} \\sum_{i=1}^k C_i X_i$. These type of sums appear in the analysis of stochastic recursions, including weighted branching processes and autoregressive processes. In particular, we derive conditions under which $$P(M_N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0301","kind":"arxiv","version":3},"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"}