{"paper":{"title":"An integral test on time dependent local extinction for super-coalescing Brownian motion with Lebesgue initial measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hui He, Xiaowen Zhou, Zenghu Li","submitted_at":"2009-11-04T10:40:30Z","abstract_excerpt":"This paper concerns the almost sure time dependent local extinction behavior for super-coalescing Brownian motion $X$ with $(1+\\beta)$-stable branching and Lebesgue initial measure on $\\bR$. We first give a representation of $X$ using excursions of a continuous state branching process and Arratia's coalescing Brownian flow. For any nonnegative, nondecreasing and right continuous function $g$, put\n  \\tau:=\\sup \\{t\\geq 0: X_t([-g(t),g(t)])>0 \\}. We prove that $\\bP\\{\\tau=\\infty\\}=0$ or 1 according as the integral $\\int_1^\\infty g(t)t^{-1-1/\\beta} dt$ is finite or infinite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0774","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"}