Continuous-discrete smoothing of diffusions
Abstract
Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the process, consistent with the observations. We derive a novel Markov Chain Monte Carlo algorithm to sample from the exact smoothing distribution. The resulting algorithm is called the Backward Filtering Forward Guiding (BFFG) algorithm. We extend the algorithm to include parameter estimation. The proposed method relies on guided proposals introduced in Schauer et al. (2017). We illustrate its efficiency in a number of challenging problems.
Cite
@article{arxiv.1712.03807,
title = {Continuous-discrete smoothing of diffusions},
author = {Marcin Mider and Moritz Schauer and Frank van der Meulen},
journal= {arXiv preprint arXiv:1712.03807},
year = {2024}
}
Comments
Revised article with additional author Marcin Mider. Article contains an animated figure