{"paper":{"title":"Modeling stationary data by a class of generalised Ornstein-Uhlenbeck processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","stat.TH"],"primary_cat":"math.ST","authors_text":"Alejandra Caba\\~na, Argimiro Arratia, Enrique M. Caba\\~na","submitted_at":"2012-10-01T08:54:21Z","abstract_excerpt":"An Ornstein-Uhlenbeck (OU) process can be considered as a continuous time interpolation of the discrete time AR$(1)$ process. Departing from this fact, we analyse in this work the effect of iterating OU treated as a linear operator that maps a Wiener process onto Ornstein-Uhlenbeck process, so as to build a family of higher order Ornstein-Uhlenbeck processes, OU$(p)$, in a similar spirit as the higher order autoregressive processes AR$(p)$. We show that for $p \\ge 2$ we obtain in general a process with covariances different than those of an AR$(p)$, and that for various continuous time process"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0312","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"}