{"paper":{"title":"Extremes of $q$-Ornstein-Uhlenbeck processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yizao Wang","submitted_at":"2016-09-01T18:27:02Z","abstract_excerpt":"The $q$-Ornstein-Uhlenbeck processes, $q\\in(-1,1)$, are a family of stationary Markov processes that converge weakly to the standard Ornstein-Uhlenbeck process as $q$ tends to 1. It has been noticed recently that in terms of path properties, however, for each $q$ fixed the $q$-Ornstein-Uhlenbeck process behaves qualitatively different from their Gaussian counterpart in several aspects. Here, two limit theorems on the extremes of $q$-Ornstein-Uhlenbeck processes are established. Both results are based on the weak convergence of the tangent process at the lower boundary, a positive self-similar "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00338","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"}