{"paper":{"title":"Strong renewal theorems with infinite mean beyond local large deviations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Zhiyi Chi","submitted_at":"2015-05-28T10:05:06Z","abstract_excerpt":"Let $F$ be a distribution function on the line in the domain of attraction of a stable law with exponent $\\alpha\\in(0,1/2]$. We establish the strong renewal theorem for a random walk $S_1,S_2,\\ldots$ with step distribution $F$, by extending the large deviations approach in Doney [Probab. Theory Related Fileds 107 (1997) 451-465]. This is done by introducing conditions on $F$ that in general rule out local large deviations bounds of the type $\\mathbb{P}\\{S_n\\in(x,x+h]\\}=O(n)\\overline{F}(x)/x$, hence are significantly weaker than the boundedness condition in Doney (1997). We also give applicatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07622","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"}