In this article we consider a Monte-Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can return online estimates of the filtering distribution with no time-discretization bias and finite variance. Our approach is based upon a novel double application of the randomization methods of Rhee and Glynn (Operat. Res.63, 2015) along with the multilevel particle filter (MLPF) approach of Jasra et al. (SIAM J. Numer. Anal.55, 2017). A numerical comparison of our new approach with the MLPF, on a single processor, shows that similar errors are possible for a mild increase in computational cost. However, the new method scales strongly to arbitrarily many processors.
Bibliographical noteKAUST Repository Item: Exported on 2022-07-05
Acknowledgements: A. J. and F. Y. were supported by KAUST baseline funding. K. J. H. L. and A. J. were supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR), under field work proposal number ERKJ333.
ASJC Scopus subject areas
- Applied Mathematics
- Statistics and Probability