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Volume 23, Issue 5
A Backward Doubly Stochastic Differential Equation Approach for Nonlinear Filtering Problems

Feng Bao, Yanzhao Cao & Weidong Zhao

DOI: 10.4208/cicp.OA-2017-0084

Commun. Comput. Phys., 23 (2018), pp. 1573-1601.

Published online: 2018-04

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  • Abstract

A backward doubly stochastic differential equation (BDSDE) based nonlinear filtering method is considered. The solution of the BDSDE is the unnormalized density function of the conditional expectation of the state variable with respect to the observation filtration, which solves the nonlinear filtering problem through the Kallianpur formula. A first order finite difference algorithm is constructed to solve the BSDES, which results in an accurate numerical method for nonlinear filtering problems. Numerical experiments demonstrate that the BDSDE filter has the potential to significantly outperform some of the well known nonlinear filtering methods such as particle filter and Zakai filter in both numerical accuracy and computational complexity.

  • Keywords

Nonlinear filtering problems, backward doubly stochastic differential equation, first order algorithm, quasi Monte Carlo sequence.

  • AMS Subject Headings

65C30, 65K10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-23-1573, author = {Feng Bao, Yanzhao Cao and Weidong Zhao}, title = {A Backward Doubly Stochastic Differential Equation Approach for Nonlinear Filtering Problems}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {5}, pages = {1573--1601}, abstract = {

A backward doubly stochastic differential equation (BDSDE) based nonlinear filtering method is considered. The solution of the BDSDE is the unnormalized density function of the conditional expectation of the state variable with respect to the observation filtration, which solves the nonlinear filtering problem through the Kallianpur formula. A first order finite difference algorithm is constructed to solve the BSDES, which results in an accurate numerical method for nonlinear filtering problems. Numerical experiments demonstrate that the BDSDE filter has the potential to significantly outperform some of the well known nonlinear filtering methods such as particle filter and Zakai filter in both numerical accuracy and computational complexity.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0084}, url = {http://global-sci.org/intro/article_detail/cicp/11227.html} }
TY - JOUR T1 - A Backward Doubly Stochastic Differential Equation Approach for Nonlinear Filtering Problems AU - Feng Bao, Yanzhao Cao & Weidong Zhao JO - Communications in Computational Physics VL - 5 SP - 1573 EP - 1601 PY - 2018 DA - 2018/04 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2017-0084 UR - https://global-sci.org/intro/article_detail/cicp/11227.html KW - Nonlinear filtering problems, backward doubly stochastic differential equation, first order algorithm, quasi Monte Carlo sequence. AB -

A backward doubly stochastic differential equation (BDSDE) based nonlinear filtering method is considered. The solution of the BDSDE is the unnormalized density function of the conditional expectation of the state variable with respect to the observation filtration, which solves the nonlinear filtering problem through the Kallianpur formula. A first order finite difference algorithm is constructed to solve the BSDES, which results in an accurate numerical method for nonlinear filtering problems. Numerical experiments demonstrate that the BDSDE filter has the potential to significantly outperform some of the well known nonlinear filtering methods such as particle filter and Zakai filter in both numerical accuracy and computational complexity.

Feng Bao, Yanzhao Cao and Weidong Zhao. (2018). A Backward Doubly Stochastic Differential Equation Approach for Nonlinear Filtering Problems. Communications in Computational Physics. 23 (5). 1573-1601. doi:10.4208/cicp.OA-2017-0084
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