{"paper":{"title":"Spectral densities describing off-white noises","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Boris Tsirelson","submitted_at":"2001-04-02T19:56:01Z","abstract_excerpt":"For the white noise, the spectral density is constant, and the past (restriction to (-\\infty,0)) is independent from the future (restriction to (0,+\\infty)). If the spectral density is not too far from being constant, then dependence between the past and the future can be eliminated by an equivalent measure change; that is called an off-white noise. I derive from well-known results a necessary and sufficient condition for a spectral density to describe an off-white noise."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0104027","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"}