{"paper":{"title":"Integral criteria for Strong Renewal Theorems with infinite mean","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Zhiyi Chi","submitted_at":"2013-12-20T19:44:11Z","abstract_excerpt":"Let $F$ be a probability measure on $\\mathbb{R}$ in the domain of attraction of a stable law with exponent $\\alpha\\in (0, 1)$. We establish integral criteria on $F$ that significantly expand the probabilistic approach to Strong Renewal Theorems (SRTs). The criterion for $\\alpha \\in (0,1/2]$ is much weaker than currently available ones and in some cases provides sufficient and necessary conditions for the SRT. The criterion for $\\alpha \\in (1/2, 1)$ establishes the SRT in full generality and in a unified way, barring the Limit Local Theorems employed. As an application, for infinitely divisible"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6089","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"}