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math.NA2025
High-dimensional Bayesian filtering through deep density approximation
Kasper Bågmark, Filip Rydin
In this work, we systematically benchmark two recently developed deep density methods for nonlinear filtering. We model the filtering density of a discretely observed stochastic di…
math.NA2025
Nonlinear filtering based on density approximation and deep BSDE prediction
Kasper Bågmark, 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.NA2024
A convergent scheme for the Bayesian filtering problem based on the Fokker--Planck equation and deep splitting
Kasper Bågmark, 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, and…