{"paper":{"title":"Boundary crossing probabilities for $(q,d)$-Slepian-processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Andreas Gegg, Wolfgang Bischoff","submitted_at":"2016-07-25T13:29:34Z","abstract_excerpt":"For $0<q< d$ fixed let $W^{[q,d]}=(W^{[q,d]}_t)_{t\\in {[q,d]}}$ be a $(q,d)$-Slepian-process defined as centered, stationary Gaussian process with continuous sample paths and covariance\n  \\begin{align*} C_{W^{[q,d]}}(s,s+t) = (1-\\frac{t}{q})^+, \\quad q\\leq s\\leq s+t\\leq d.\n  \\end{align*} Note that\n  \\begin{align*} \\frac{1}{\\sqrt{q}}(B_t-B_{t-q})_{t\\in [q,d]}, \\end{align*} where $B_t$ is standard Brownian motion, is a $(q,d)$-Slepian-process. In this paper we prove an analytical formula for the boundary crossing probability $\\mathbb{P}\\left(W^{[q,d]}_t > g(t) \\; \\text{for some } t\\in[q,d]\\right"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07260","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"}