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Unbiased estimation of the solution to Zakai’s equation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ruzayqat Hamza M. & Jasra Ajay, 2020. "Unbiased estimation of the solution to Zakai’s equation," Monte Carlo Methods and Applications, De Gruyter, vol. 26(2), pages 113-129, June.
    • Handle: RePEc:bpj:mcmeap:v:26:y:2020:i:2:p:113-129:n:3
    DOI: 10.1515/mcma-2020-2061
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    References listed on IDEAS

    as
    1. McLeish, Don, 2011. "A general method for debiasing a Monte Carlo estimator," Monte Carlo Methods and Applications, De Gruyter, vol. 17(4), pages 301-315, December.
    2. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    3. Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.
    Full references (including those not matched with items on IDEAS)

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