{"paper":{"title":"Large deviations and laws of the iterated logarithm for the local times of additive stable processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xia Chen","submitted_at":"2006-03-07T14:56:59Z","abstract_excerpt":"We study the upper tail behaviors of the local times of the additive stable processes. Let $X_1(t),...,X_p(t)$ be independent, d-dimensional symmetric stable processes with stable index $0<\\alpha\\le 2$ and consider the additive stable process $\\bar{X}(t_1,...,t_p)=X_1(t_1)+... +X_p(t_p)$. Under the condition $d<\\alpha p$, we obtain a precise form of the large deviation principle for the local time \\[\\eta^x([0,t]^p)=\\int_0^t...\\int_0^t\\delta_x\\bigl(X_1(s_1)+... +X_p(s_p)\\bigr) ds_1... ds_p\\] of the multiparameter process $\\bar{X}(t_1,...,t_p)$, and for its supremum norm $\\sup_{x\\in\\mathbb{R}^d}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603159","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"}