{"paper":{"title":"Uniform LAN property of locally stable L\\'{e}vy process observed at high frequency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexey M. Kulik, Dmytro Ivanenko, Hiroki Masuda","submitted_at":"2014-11-06T07:56:27Z","abstract_excerpt":"Suppose we have a high-frequency sample from the L\\'{e}vy process of the form $X_t^\\theta=\\beta t+\\gamma Z_t+U_t$, where $Z$ is a possibly asymmetric locally $\\alpha$-stable L\\'{e}vy process, and $U$ is a nuisance L\\'{e}vy process less active than $Z$. We prove the LAN property about the explicit parameter $\\theta=(\\beta,\\gamma)$ under very mild conditions without specific form of the L\\'{e}vy measure of $Z$, thereby generalizing the LAN result of A\\\"{\\i}t-Sahalia and Jacod (2007). In particular, it is clarified that a non-diagonal norming may be necessary in the truly asymmetric case. Due to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1516","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"}