{"paper":{"title":"The General Stationary Gaussian Markov Process","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bob Wolpert, Larry Brown, Larry Shepp, Philip Ernst","submitted_at":"2014-01-01T04:59:19Z","abstract_excerpt":"We find the class, ${\\cal{C}}_k, k \\ge 0$, of all zero mean stationary Gaussian processes, $Y(t), ~t \\in \\reals$ with $k$ derivatives, for which\n  \\begin{equation} Z(t) \\equiv (Y^{(0)}(t), Y^{(1)}(t), \\ldots, Y^{(k)}(t) ), ~ t \\ge 0 \\end{equation}\n  \\noindent is a $(k+1)$-vector Markov process. (here, $Y^{(0)}(t) = Y(t)$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0251","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"}