Nonlinear filtering based on density approximation and deep BSDE prediction
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911605097234432 |
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| author | Bågmark, Kasper Andersson, Adam Larsson, Stig |
| author_facet | Bågmark, Kasper Andersson, Adam Larsson, Stig |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear filtering based on density approximation and deep BSDE prediction Bågmark, Kasper Andersson, Adam Larsson, Stig Numerical Analysis Computation Machine Learning 60G25, 60G35, 62F15, 62G07, 62M20, 65C30, 65M75, 68T07 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. |
| title | Nonlinear filtering based on density approximation and deep BSDE prediction |
| topic | Numerical Analysis Computation Machine Learning 60G25, 60G35, 62F15, 62G07, 62M20, 65C30, 65M75, 68T07 |
| url | https://arxiv.org/abs/2508.10630 |