{"paper":{"title":"The weak convergence of regenerative processes using some excursion path decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amaury Lambert, Florian Simatos","submitted_at":"2012-02-13T21:44:00Z","abstract_excerpt":"We consider regenerative processes with values in some Polish space. We define their \\epsilon-big excursions as excursions e such that f(e)>\\epsilon, where f is some given functional on the space of excursions which can be thought of as, e.g., the length or the height of e. We establish a general condition that guarantees the convergence of a sequence of regenerative processes involving the convergence of \\epsilon-big excursions and of their endpoints, for all \\epsilon in a countable set whose closure contains 0. Finally, we provide various sufficient conditions on the excursion measures of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2878","kind":"arxiv","version":3},"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"}