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math.NA2026
Nonlinear filtering based on density approximation and deep BSDE prediction
Kasper BÃ¥gmark, Adam Andersson, Stig Larsson
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…
math.NA2026
A convergent scheme for the Bayesian filtering problem based on the Fokker--Planck equation and deep splitting
Kasper BÃ¥gmark, Adam Andersson, Stig Larsson +1
A numerical scheme for approximating the nonlinear filtering density is introduced and its convergence rate is established, theoretically under a parabolic Hörmander condition, an…
math.NA2025
The deep multi-FBSDE method: a robust deep learning method for coupled FBSDEs
Kristoffer Andersson, Adam Andersson, Cornelis W. Oosterlee
We introduce the deep multi-FBSDE method for robust approximation of coupled forward-backward stochastic differential equations (FBSDEs), focusing on cases where the deep BSDE meth…