{"paper":{"title":"A general approach to small deviation via concentration of measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ehsan Azmoodeh, Lauri Viitasaari","submitted_at":"2014-07-14T07:50:51Z","abstract_excerpt":"We provide a general approach to obtain upper bounds for small deviations $ \\mathbb{P}(\\Vert y \\Vert \\le \\epsilon)$ in different norms, namely the supremum and $\\beta$- H\\\"older norms. The large class of processes $y$ under consideration takes the form $y_t= X_t + \\int_0^t a_s d s$, where $X$ and $a$ are two possibly dependent stochastic processes. Our approach provides an upper bound for small deviations whenever upper bounds for the \\textit{concentration of measures} of $L^p$- norm of random vectors built from increments of the process $X$ and \\textit{large deviation} estimates for the proce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3553","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"}