{"paper":{"title":"Small Time Convergence of Subordinators with Regularly or Slowly Varying Canonical Measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross Maller, Tanja Schindler","submitted_at":"2018-06-26T02:24:48Z","abstract_excerpt":"We consider subordinators $X_\\alpha=(X_\\alpha(t))_{t\\ge 0}$ in the domain of attraction at 0 of a stable subordinator $(S_\\alpha(t))_{t\\ge 0}$ (where $\\alpha\\in(0,1)$); thus, with the property that $\\overline{\\Pi}_\\alpha$, the tail function of the canonical measure of $X_\\alpha$, is regularly varying of index $-\\alpha\\in (-1,0)$ as $x\\downarrow 0$. We also analyse the boundary case, $\\alpha=0$, when $\\overline{\\Pi}_\\alpha$ is slowly varying at 0. When $\\alpha\\in(0,1)$, we show that $(t \\overline{\\Pi}_\\alpha (X_\\alpha(t)))^{-1}$ converges in distribution, as $t\\downarrow 0$, to the random varia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09763","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"}