Nonlinear filtering based on density approximation and deep BSDE prediction

• URL: http://arxiv.org/abs/2508.10630v1
• Date: Thu, 14 Aug 2025 13:31:05 GMT
• Title: Nonlinear filtering based on density approximation and deep BSDE prediction
• Authors: Kasper Bågmark, Adam Andersson, Stig Larsson,
• Abstract summary: A novel approximate Bayesian filter based on backward differential equations is introduced.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 mixed a priori-a posteriori error bound is proved under an elliptic condition. The theoretical convergence rate is confirmed in two numerical examples.

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