{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/multilevel-ensemble-kalman-bucy-filters","title":"Multilevel Ensemble Kalman-Bucy Filters","arxiv_id":"2011.04342","date":"2020-11-09","proceeding":null,"authors":["Neil K. Chada","Ajay Jasra","Fangyuan Yu"],"abstract":"In this article we consider the linear filtering problem in continuous-time. We develop and apply multilevel Monte Carlo (MLMC) strategies for ensemble Kalman-Bucy filters (EnKBFs). These filters can be viewed as approximations of conditional McKean-Vlasov-type diffusion processes. They are also interpreted as the continuous-time analogue of the \\textit{ensemble Kalman filter}, which has proven to be successful due to its applicability and computational cost. We prove that an ideal version of our multilevel EnKBF can achieve a mean square error (MSE) of $\\mathcal{O}(\\epsilon^2), \\ \\epsilon>0$ with a cost of order $\\mathcal{O}(\\epsilon^{-2}\\log(\\epsilon)^2)$. In order to prove this result we provide a Monte Carlo convergence and approximation bounds associated to time-discretized EnKBFs. This implies a reduction in cost compared to the (single level) EnKBF which requires a cost of $\\mathcal{O}(\\epsilon^{-3})$ to achieve an MSE of $\\mathcal{O}(\\epsilon^2)$. We test our theory on a linear problem, which we motivate through high-dimensional examples of order $\\sim \\mathcal{O}(10^4)$ and $\\mathcal{O}(10^5)$.","url_abs":"https://arxiv.org/abs/2011.04342v2","url_pdf":"https://arxiv.org/pdf/2011.04342v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"multilevel-ensemble-kalman-bucy-filters","repo_url":"https://github.com/fangyuan-ksgk/Multilevel-Ensemble-Kalman-Bucy-Filter","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}