{"paper":{"title":"On the infimum attained by the reflected fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kamil Marcin Kosi\\'nski, Krzysztof D\\k{e}bicki","submitted_at":"2013-10-05T17:20:45Z","abstract_excerpt":"Let $\\{B_H(t):t\\ge 0\\}$ be a fractional Brownian motion with Hurst parameter $H\\in(\\frac{1}{2},1)$. For the storage process $Q_{B_H}(t)=\\sup_{-\\infty\\le s\\le t} \\left(B_H(t)-B_H(s)-c(t-s)\\right)$ we show that, for any $T(u)>0$ such that $T(u)=o(u^\\frac{2H-1}{H})$, \\[\\mathbb P (\\inf_{s\\in[0,T(u)]} Q_{B_H}(s)>u)\\sim\\mathbb P(Q_{B_H}(0)>u),\\quad\\text{as}\\quad u\\to\\infty.\\] This finding, known in the literature as the strong Piterbarg property, is in line with previously observed properties of storage processes with self-similar and infinitely divisible input without Gaussian component."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1496","kind":"arxiv","version":2},"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"}