{"paper":{"title":"Comparison for upper tail probabilities of random series","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fuchang Gao, Xiangfeng Yang, Zhenxia Liu","submitted_at":"2013-02-11T10:19:40Z","abstract_excerpt":"Let $\\{\\xi_n\\}$ be a sequence of independent and identically distributed random variables. In this paper we study the comparison for two upper tail probabilities $\\mathbb{P}\\{\\sum_{n=1}^{\\infty}a_n|\\xi_n|^p\\geq r\\}$ and $\\mathbb{P}\\{\\sum_{n=1}^{\\infty}b_n|\\xi_n|^p\\geq r\\}$ as $r\\rightarrow\\infty$ with two different real series $\\{a_n\\}$ and $\\{b_n\\}.$ The first result is for Gaussian random variables $\\{\\xi_n\\},$ and in this case these two probabilities are equivalent after suitable scaling. The second result is for more general random variables, thus a weaker form of equivalence (namely, loga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2435","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"}