{"paper":{"title":"Precise asymptotics for large deviations of integral forms","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xiangfeng Yang","submitted_at":"2012-11-23T21:17:47Z","abstract_excerpt":"For suitable families of locally infinitely divisible Markov processes $\\{\\xi^{{\\epsilon}}_t\\}_{0\\leq t\\leq T}$ with frequent small jumps depending on a small parameter $\\epsilon>0,$ precise asymptotics for large deviations of integral forms $\\mathbb{E}^{\\epsilon}[\\exp\\{{\\epsilon}^{-1}F(\\xi^{\\epsilon})\\}]$ are proved for smooth functionals $F.$ The main ingredient of the proof in this paper is a recent result regarding the asymptotic expansions of the expectations $\\mathbb{E}^{\\epsilon}[G(\\xi^{\\epsilon})\\}]$ for smooth $G.$ Several connections between these large deviation asymptotics and part"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5610","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"}