{"paper":{"title":"On exceedance times for some processes with dependent increments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sergey Foss, S{\\o}ren Asmussen","submitted_at":"2012-05-25T19:56:18Z","abstract_excerpt":"Let ${Z_n}_{n\\ge 0}$ be a random walk with a negative drift and i.i.d. increments with heavy-tailed distribution and let $M=\\sup_{n\\ge 0}Z_n$ be its supremum. Asmussen & Kl{\\\"u}ppelberg (1996) considered the behavior of the random walk given that $M>x$, for $x$ large, and obtained a limit theorem, as $x\\to\\infty$, for the distribution of the quadruple that includes the time $\\rtreg=\\rtreg(x)$ to exceed level $x$, position $Z_{\\rtreg}$ at this time, position $Z_{\\rtreg-1}$ at the prior time, and the trajectory up to it (similar results were obtained for the Cram\\'er-Lundberg insurance risk proc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5793","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"}