{"paper":{"title":"Strassen's local law of the iterated logarithm for the generalized fractional Brownian motion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ran Wang, Yimin Xiao","submitted_at":"2024-11-24T01:57:38Z","abstract_excerpt":"Let $X:=\\{X(t)\\}_{t\\ge0}$ be a generalized fractional Brownian motion given by $$\n  \\{X(t)\\}_{t\\ge0}\\overset{d}{=}\\left\\{ \\int_{\\mathbb R} \\left((t-u)_+^{\\alpha}-(-u)_+^{\\alpha} \\right) |u|^{-\\gamma/2} B(du) \\right\\}_{t\\ge0}, $$ with parameters $\\gamma \\in (0, 1)$ and $\\alpha\\in \\left(-1/2+ \\gamma/2, \\, 1/2+\\gamma/2\\right)$. This process was introduced by Pang and Taqqu (2019) as the scaling limit of a class of power-law shot noise processes. The parameters $\\alpha$ and $\\gamma$ govern the probabilistic and statistical properties of $X$. In particular, the parameter $\\gamma$ breaks the station"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15681","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.15681/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}