mlsanityData to 14 Oct 2026

Nonlinear filtering based on density approximation and deep BSDE prediction

arXiv 2508.10630 ↗First posted 14 Aug 2025math.NA cs.NA stat.COcited by 1

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Abstract (arXiv)

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 H"ormander condition. The theoretical convergence rate is confirmed in two numerical examples.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 21 of its 52 references that are in the map. First posted on arXiv 14 Aug 2025.

Builds on

21 of 52 references.

References · 21

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9 more
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Citing papers per year: 2025: 1.

1 paper.

  1. 2025High-dimensional Bayesian filtering through deep density approximationcited by 0