{"paper":{"title":"Asymptotic results for sample autocovariance functions and extremes of integrated generalized Ornstein-Uhlenbeck processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Vicky Fasen","submitted_at":"2010-02-23T07:08:25Z","abstract_excerpt":"We consider a positive stationary generalized Ornstein--Uhlenbeck process \\[V_t=\\mathrm{e}^{-\\xi_t}\\biggl(\\int_0^t\\mathrm{e}^{\\xi_{s-}}\\ ,\\mathrm{d}\\eta_s+V_0\\biggr)\\qquadfor t\\geq0,\\] and the increments of the integrated generalized Ornstein--Uhlenbeck process $I_k=\\int_{k-1}^k\\sqrt{V_{t-}} \\mathrm{d}L_t$, $k\\in\\mathbb{N}$, where $(\\xi_t,\\eta_t,L_t)_{t\\geq0}$ is a three-dimensional L\\'{e}vy process independent of the starting random variable $V_0$. The genOU model is a continuous-time version of a stochastic recurrence equation. Hence, our models include, in particular, continuous-time versio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4257","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1002.4257/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}