{"paper":{"title":"Weak Convergence of Subordinators to Extremal Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andreas L\\\"opker, Offer Kella","submitted_at":"2012-10-08T10:26:51Z","abstract_excerpt":"For certain subordinators $(X_t)_{t\\ge 0}$ it is shown that the process $(-t\\log X_{ts})_{s>0}$ tends to an extremal process $(\\hat\\eta_s)_{s>0}$ in the sense of convergence of the finite dimensional distributions. Additionally it is also shown that $(z\\wedge(-t\\log X_{ts}))_{s\\ge 0}$ converges weakly to $(z\\wedge\\hat\\eta_s)_{s\\ge0}$ in $\\mathcal{D}[0,\\infty)$, the space of c\\`{a}dl\\`{a}g functions equipped with Skorohod's $J_1$ metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2218","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"}