Splitting-up Spectral Method for Nonlinear Filtering Problems with Correlation Noises

In this paper, we study nonlinear filtering problems via solving their corresponding Zakai equations. Using the splitting-up technique, we approximate the Zakai equation with two equations consisting of a first-order stochastic partial differential equation and a deterministic second-order partial d...

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Bibliographic Details
Published in:Journal of scientific computing 2022-10, Vol.93 (1), p.25, Article 25
Main Authors: Zhang, Fengshan, Zou, Yongkui, Chai, Shimin, Zhang, Ran, Cao, Yanzhao
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Discretization
Dynamical systems
Filtration
Finite difference method
Galerkin method
Iterative methods
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Noise
Partial differential equations
Signal processing
Spectral methods
Splitting
Stochastic models
Theoretical
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Summary:In this paper, we study nonlinear filtering problems via solving their corresponding Zakai equations. Using the splitting-up technique, we approximate the Zakai equation with two equations consisting of a first-order stochastic partial differential equation and a deterministic second-order partial differential equation. For the splitting-up equations, we use a spectral Galerkin method for the spatial discretization and a finite difference scheme for the temporal discretization. The main results are an error estimate for the semi-discretized scheme with respect to the spatial variable, and an error estimate for the full discretized scheme. To improve the numerical performance, we apply an adaptive technique to accurately locate the support domain of the solution in each time iteration. Finally, we present numerical experiments to demonstrate our theoretical analysis.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-022-01994-6