{"paper":{"title":"Criteria for Borel-Cantelli lemmas with applications to Markov chains and dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Rio (UVSQ), Florence Merlev\\`ede (LAMA), J\\'er\\^ome Dedecker (MAP5 - UMR 8145)","submitted_at":"2019-04-03T08:53:53Z","abstract_excerpt":"Let (X k) be a strictly stationary sequence of random variables with values in some Polish space E and common marginal $\\mu$, and (A k) k>0 be a sequence of Borel sets in E. In this paper, we give some conditions on (X k) and (A k) under which the events {X k $\\in$ A k } satisfy the Borel-Cantelli (or strong Borel-Cantelli) property. In particular we prove that, if $\\mu$(lim sup n A n) > 0, the Borel-Cantelli property holds for any absolutely regular sequence. In case where the A k 's are nested, we show, on some examples, that a rate of convergence of the mixing coefficients is needed. Finall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01850","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"}