{"paper":{"title":"Fractal-Dimensional Properties of Subordinators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Adam Barker","submitted_at":"2017-06-21T12:09:56Z","abstract_excerpt":"This work looks at the box-counting dimension of sets related to subordinators (non-decreasing L\\'evy processes). It was recently shown in [Savov, 2014] that almost surely $\\lim_{\\delta\\to0}U(\\delta)N(t,\\delta) = t$, where $N(t,\\delta)$ is the minimal number of boxes of size at most $\\delta$ needed to cover a subordinator's range up to time $t$, and $U(\\delta)$ is the subordinator's renewal function. Our main result is a central limit theorem (CLT) for $N(t,\\delta)$, complementing and refining work in [Savov, 2014].\n  Box-counting dimension is defined in terms of $N(t,\\delta)$, but for subordi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06850","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"}