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Unbiased filtering of a class of partially observed diffusions

Part of: Probabilistic methods, simulation and stochastic differential equations Markov processes

Published online by Cambridge University Press:  15 June 2022

Ajay Jasra ,
Kody J. H. Law  and
Fangyuan Yu
Ajay Jasra*
Affiliation:
King Abdullah University of Science and Technology
Kody J. H. Law*
Affiliation:
University of Manchester
Fangyuan Yu*
Affiliation:
King Abdullah University of Science and Technology
*
*Postal address: Computer, Electrical and Mathematical Sciences and Engineering Division, Thuwal, 23955, KSA.
**Postal address: School of Mathematics, Manchester, M13 9PL, UK. Email address: kodylaw@gmail.com
*Postal address: Computer, Electrical and Mathematical Sciences and Engineering Division, Thuwal, 23955, KSA.
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Abstract

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.

Keywords

Partially observed diffusionsrandomization methodsmultilevel Monte Carlo

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 3 , September 2022 , pp. 661 - 687
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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References

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