{"paper":{"title":"Joint law of the hitting time, overshoot and undershoot for a L\\'evy process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Laure Coutin, Waly Ngom","submitted_at":"2016-03-08T12:57:47Z","abstract_excerpt":"Let be $(X_t, t\\geq 0)$ be a L\\'evy process which is the sum of a Brownian motion with drift and a compound Poisson process. We consider the first passage time $\\tau_x$ at a fixed level $x>0$ by $(X_t, t\\geq 0)$ and $K_x:= X_{\\tau_x}-x$ the overshoot and $L_x:= x-X_{\\tau_x^-}$ the undershoot. We first study the regularity of the density of the first passage time. Secondly, we calculate the joint law of $(\\tau_x, K_x, L_x).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02506","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"}