• DOI:10.48550/arXiv.2206.03369
• Corpus ID: 249431935

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

@article{Chopin2022ComputationalDH,
  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},
  journal={ArXiv},
  year={2022},
  volume={abs/2206.03369}
}

• N. Chopin, Andras Fulop, +1 author Alexandre Hoang Thiery
• Published 7 June 2022
• Mathematics
• ArXiv

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 prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, or if the state dimension is large.