{"paper":{"title":"Excursions of a spectrally negative L\\'evy process from a two-point set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Matija Vidmar","submitted_at":"2018-09-03T11:39:31Z","abstract_excerpt":"Let $a\\in (0,\\infty)$. For a spectrally negative L\\'evy process $X$ with infinite variation paths the resolvent of the process killed on hitting the two-point set $V=\\{-a,a\\}$ is identified. When further $X$ has no diffusion component the Laplace transforms of the entrance laws of the excursion measures of $X$ from $V$ are determined. This is then applied to establishing the Laplace transform of the amount of time that elapses between the last visit of $X$ to a given point $x$, before hitting some other point $y>x$, and the hitting time of $y$. All the expressions are explicit and tractable in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00560","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"}