{"paper":{"title":"Uniform Local Asymptotics for L\\'evy Processes with Subexponential Jumps","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hao Wu, Wei Xu","submitted_at":"2026-08-12T04:34:46Z","abstract_excerpt":"This paper is devoted to unifying the uniform local large-deviation asymptotics for a centered L\\'evy process $X$ with subexponential jumps. Our results assert that for any $\\theta,\\delta_0>0$ and $K\\geq0$, $$\\lim_{t\\to\\infty}\\sup_{x\\geq\\theta t}\\sup_{|y|\\leq Kb(x)}\\sup_{\\delta\\in[\\delta_0,\\infty]}\\sup_{0<s\\leq t}\\bigg|\\frac{\\mathbf P\\big(X_s\\in(x-y,x-y+\\delta]\\big)}{s\\cdot\\mathbf P\\big(X_1\\in(x,x+\\delta]\\big)}-1\\bigg|=0,$$ where the natural-scale function $b$ satisfies a polynomial growth condition. This provides a continuous-time and simultaneously uniform analogue of the results of Denisov "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11637","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.11637/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}