{"paper":{"title":"Optimization Based Methods for Partially Observed Chaotic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OC"],"primary_cat":"stat.ME","authors_text":"Ajay Jasra, Alexandros Beskos, Dan Crisan, Daniel Paulin","submitted_at":"2017-02-08T15:56:20Z","abstract_excerpt":"In this paper we consider filtering and smoothing of partially observed chaotic dynamical systems that are discretely observed, with an additive Gaussian noise in the observation. These models are found in a wide variety of real applications and include the Lorenz 96' model. In the context of a fixed observation interval $T$, observation time step $h$ and Gaussian observation variance $\\sigma_Z^2$, we show under assumptions that the filter and smoother are well approximated by a Gaussian with high probability when $h$ and $\\sigma^2_Z h$ are sufficiently small. Based on this result we show that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02484","kind":"arxiv","version":3},"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"}