{"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/unbiased-and-multilevel-methods-for-a-class","title":"Unbiased and Multilevel Methods for a Class of Diffusions Partially Observed via Marked Point Processes","arxiv_id":"2311.09875","date":"2023-11-16","proceeding":null,"authors":["Miguel Alvarez","Ajay Jasra","Hamza Ruzayqat"],"abstract":"In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity driven by a diffusion, with the associated marks also depending upon the diffusion process. We assume that one must resort to time-discretizing the diffusion process and develop particle and multilevel particle filters to recursively approximate the filter. In particular, we prove that our multilevel particle filter can achieve a mean square error (MSE) of $\\mathcal{O}(\\epsilon^2)$ ($\\epsilon>0$ and arbitrary) with a cost of $\\mathcal{O}(\\epsilon^{-2.5})$ versus using a particle filter which has a cost of $\\mathcal{O}(\\epsilon^{-3})$ to achieve the same MSE. We then show how this methodology can be extended to give unbiased (that is with no time-discretization error) estimators of the filter, which are proved to have finite variance and with high-probability have finite cost. Finally, we extend our methodology to the problem of online static-parameter estimation.","url_abs":"https://arxiv.org/abs/2311.09875v1","url_pdf":"https://arxiv.org/pdf/2311.09875v1.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":"unbiased-and-multilevel-methods-for-a-class","repo_url":"https://github.com/maabs/multilevel-for-diffusions-observed-via-marked-point-processes","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}