{"ID":2882336,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.10630","arxiv_id":"2508.10630","title":"Nonlinear filtering based on density approximation and deep BSDE prediction","abstract":"A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using the well-known deep BSDE method and neural networks. The method is trained offline, which means that it can be applied online with new observations. A hybrid a priori-a posteriori error bound is proved under a parabolic Hörmander condition. The theoretical convergence rate is confirmed in two numerical examples.","short_abstract":"A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using the well-known deep BSDE method and neural networks. The method is trained offl...","url_abs":"https://arxiv.org/abs/2508.10630","url_pdf":"https://arxiv.org/pdf/2508.10630v2","authors":"[\"Kasper Bågmark\",\"Adam Andersson\",\"Stig Larsson\"]","published":"2025-08-14T13:31:05Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"stat.CO\",\"stat.ML\"]","methods":"[]","has_code":false}