{"paper":{"title":"On the small-time behavior of subordinators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Andreas L\\\"opker, Shaul K. Bar-Lev, Wolfgang Stadje","submitted_at":"2012-07-25T07:11:54Z","abstract_excerpt":"We prove several results on the behavior near t=0 of $Y_t^{-t}$ for certain $(0,\\infty)$-valued stochastic processes $(Y_t)_{t>0}$. In particular, we show for L\\'{e}vy subordinators that the Pareto law on $[1,\\infty)$ is the only possible weak limit and provide necessary and sufficient conditions for the convergence. More generally, we also consider the weak convergence of $tL(Y_t)$ as $t\\to0$ for a decreasing function $L$ that is slowly varying at zero. Various examples demonstrating the applicability of the results are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5902","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"}