{"paper":{"title":"The first passage time problem over a moving boundary for asymptotically stable L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frank Aurzada, Tanja Kramm","submitted_at":"2013-05-06T14:09:29Z","abstract_excerpt":"We study the asymptotic tail behaviour of the first-passage time over a moving boundary for asymptotically $\\alpha$-stable L\\'evy processes with $\\alpha<1$.\n  Our main result states that if the left tail of the L\\'evy measure is regularly varying with index $- \\alpha$ and the moving boundary is equal to $1 - t^{\\gamma}$ for some $\\gamma<1/\\alpha$, then the probability that the process stays below the moving boundary has the same asymptotic polynomial order as in the case of a constant boundary. The same is true for the increasing boundary $1 + t^{\\gamma}$ with $\\gamma<1/\\alpha$ under the assum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1203","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"}