{"paper":{"title":"A deviation bound for $\\alpha$-dependent sequences with applications to intermittent maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florence Merlev\\`ede (LAMA), J Dedecker (MAP5)","submitted_at":"2016-01-21T09:42:37Z","abstract_excerpt":"We prove a deviation bound for the maximum of partial sums of functions of $\\alpha$-dependent sequences as defined in Dedecker, Gou{\\\"e}zel and Merlev{\\`e}de  (2010). As a consequence, we extend the Rosenthal inequality of Rio (2000) for $\\alpha$-mixing sequences in the sense of Rosenblatt (1956) to the larger class of $\\alpha$-dependent sequences. Starting from the deviation inequality, we obtain upper bounds for large deviations and an H{\\\"o}lderian invariance principle for the Donsker line. We illustrate our results through the example of intermittent maps of the interval, which are not $\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05567","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"}