{"paper":{"title":"Multifractal analysis for the occupation measure of stable-like processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"St\\'ephane Seuret (LAMA), Xiaochuan Yang (LAMA)","submitted_at":"2016-05-27T11:56:03Z","abstract_excerpt":"In this article, we investigate the local behaviors of the occupation measure $\\mu$ of a class of real-valued Markov processes M, defined via a SDE. This (random) measure describes the time spent in each set A $\\subset$ R by the sample paths of M. We compute the multifractal spectrum of $\\mu$, which turns out to be random, depending on the trajec-tory. This remarkable property is in sharp contrast with the results previously obtained on occupation measures of other processes (such as L{\\'e}vy processes), since the multifractal spectrum is usually determinis-tic, almost surely. In addition, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08594","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"}