{"paper":{"title":"Sample path properties of reflected Gaussian processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kamil Marcin Kosi\\'nski, Peng Liu","submitted_at":"2017-11-01T23:00:54Z","abstract_excerpt":"We consider a stationary queueing process $Q_X$ fed by a centered Gaussian process $X$ with stationary increments and variance function satisfying classical regularity conditions. A criterion when, for a given function $f$, $\\mathbb P (Q_{X}(t) > f(t)\\, \\text{ i.o.})$ equals 0 or 1 is provided. Furthermore, an Erd\\\"os-R\\'ev\\'esz type law of the iterated logarithm is proven for the last passage time $\\xi (t) = \\sup\\{s:0\\le s\\le t, Q_{X}(s)\\ge f(s)\\}$. Both of these findings extend previously known results that were only available for the case when $X$ is a fractional Brownian motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01165","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"}