Unbiased estimation of the solution to Zakai’s equation

Ruzayqat Hamza M. () and Jasra Ajay ()
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Ruzayqat Hamza M.: Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955, Saudi Arabia
Jasra Ajay: Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955, Saudi Arabia

Monte Carlo Methods and Applications, 2020, vol. 26, issue 2, 113-129

Abstract: In the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.

Keywords: Unbiased estimation; multilevel Monte Carlo; particle filters; non-linear filtering (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/mcma-2020-2061

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