Nonlinear filtering based on density approximation and deep BSDE prediction
Preprint, 2025
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.
convergence order
Hörmander's condition
Fokker--Planck equation
deep learning
Filtering problem
backward stochastic differential equations
numerical analysis
Author
Kasper Bågmark
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
University of Gothenburg
Adam Andersson
University of Gothenburg
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Stig Larsson
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
University of Gothenburg
Subject Categories (SSIF 2025)
Probability Theory and Statistics
Computational Mathematics
Mathematical Analysis
Roots
Basic sciences
Infrastructure
Chalmers e-Commons (incl. C3SE, 2020-)
DOI
10.48550/arXiv.2508.10630