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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): BAS/1/1681-01-01
Acknowledgements: King Abdullah University of Science and Technology Award identifier / Grant number: BAS/1/1681-01-01 Both authors were supported by KAUST baseline funding.