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

Nicolas Chopin, Andras Fulop, Jeremy Heng, Alexandre H. Thiery

Keywords: diffusion, filtering, monte-carlo, particle-filters, BSDE

Abstract: This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. We propose to approximate the Fully Adapted Particle Filter algorithm by solving a single auxiliary stochastic control problem prior to the data-assimilation procedure. The methodology relies on the non-linear Feynman-Kac approach to solving semi-linear partial differential equations. Numerical experiments suggest that the proposed approach can be orders of magnitude more efficient than the bootstrap particle filter in the regime when observations are highly informative.