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
Författare
Kasper Bågmark
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Göteborgs universitet
Adam Andersson
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Stig Larsson
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Göteborgs universitet
Ämneskategorier (SSIF 2025)
Sannolikhetsteori och statistik
Beräkningsmatematik
Matematisk analys
Fundament
Grundläggande vetenskaper
Infrastruktur
Chalmers e-Commons (inkl. C3SE, 2020-)
DOI
10.48550/arXiv.2508.10630