{"paper":{"title":"Thin and Thick Strip Passage Times for L\\'evy Flights and L\\'evy Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross A. Maller, Yuguang Fan","submitted_at":"2015-04-24T05:40:58Z","abstract_excerpt":"We review some of the theory relevant to passage times of one-dimensional L\\'evy processes out of bounded regions, highlighting results that are useful in physical phenomena modelled by heavy-tailed L\\'evy flights. The process is hypothesised to describe the motion of a particle on the line, starting at $0$, and exiting either a fixed interval $[-r, r]$, $r > 0$, or a time-dependent, expanding, set of intervals of the form $[-r t^\\kappa, r t^\\kappa]$, $r > 0$, $\\kappa > 0$. Asymptotic behaviour of the exit time may be as $r \\downarrow 0$ or as $r \\to \\infty$, but particular emphasis is placed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06400","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"}