@Article{CiCP-36-996,
author = {Zhang , FengshanZou , YongkuiChai , Shimin and Cao , Yanzhao},
title = {A Splitting Method for Nonlinear Filtering Problems with Diffusive and Point Process Observations},
journal = {Communications in Computational Physics},
year = {2024},
volume = {36},
number = {4},
pages = {996--1020},
abstract = {<p style="text-align: justify;">This paper aims to develop and analyze a comprehensive discretized
splitting-up numerical scheme for the Zakai equation. This equation arises from a
nonlinear filtering problem, where observations incorporate noise modeled by point
processes and Wiener processes. Initially, we introduce a regularization parameter and
employ a splitting-up approach to break down the Zakai equation into two stochastic
differential equations and a partial differential equation (PDE). Subsequently, we employ a finite difference scheme for the temporal dimension and the spectral Galerkin
method for the spatial dimension to achieve full discretization of these equations. This
results in a numerical solution for the Zakai equation using the splitting-up technique.
We demonstrate that this numerical solution converges to the exact solution with a
convergence order of $\frac{1}{2}.$ Additionally, we conduct several numerical experiments to
illustrate and validate our theoretical findings.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2024-0075},
url = {http://global-sci.org/intro/article_detail/cicp/23484.html}
}