Nonlinear filtering based on density approximation and deep BSDE prediction

Kasper Bågmark; Adam Andersson; Stig Larsson

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arXiv · 2508.10630

Nonlinear filtering based on density approximation and deep BSDE prediction

Kasper Bågmark·Adam Andersson·Stig Larsson

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

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Kasper Bågmark, Adam Andersson, Stig Larsson. 2025-08-14. Nonlinear filtering based on density approximation and deep BSDE prediction. https://arxiv.org/abs/2508.10630

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