TY - JOUR

T1 - Unbiased estimation of the solution to Zakai's equation

AU - Ruzayqat, Hamza M.

AU - Jasra, Ajay

N1 - KAUST 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.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/661826

UR - https://www.degruyter.com/view/journals/mcma/ahead-of-print/article-10.1515-mcma-2020-2061/article-10.1515-mcma-2020-2061.xml

UR - http://www.scopus.com/inward/record.url?scp=85083655983&partnerID=8YFLogxK

U2 - 10.1515/mcma-2020-2061

DO - 10.1515/mcma-2020-2061

M3 - Article

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

SN - 0929-9629

ER -