Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions

  title={Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions},
  author={Nicolas Chopin and Andras Fulop and Jeremy Heng and Alexandre Hoang Thiery},
This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable. We propose a computational framework to approximate these $h$-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter… 

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