{"paper":{"title":"On generalized Piterbarg-Berman function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Chengxiu Ling, Hong Zhang, Long Bai","submitted_at":"2019-05-23T11:51:37Z","abstract_excerpt":"This paper aims to evaluate the Piterbarg-Berman function given by $$\\mathcal{P\\!B}_\\alpha^h(x, E) = \\int_\\mathbb{R}e^z\\mathbb{P} \\left\\{{\\int_E \\mathbb{I}\\left(\\sqrt2B_\\alpha(t) - |t|^\\alpha - h(t) - z>0 \\right) {\\text{d}} t > x} \\right\\} {\\text{d}} z,\\quad x\\in[0, {mes}(E)],$$ with $h$ a drift function and $B_\\alpha$ a fractional Brownian motion (fBm) with Hurst index $\\alpha/2\\in(0,1]$, i.e., a mean zero Gaussian process with continuous sample paths and covariance function \\begin{align*} {\\mathrm{Cov}}(B_\\alpha(s), B_\\alpha(t)) = \\frac12 (|s|^\\alpha + |t|^\\alpha - |s-t|^\\alpha). \\end{align*"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09599","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"}