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Volume 15, Issue 3
Sinc-Multistep Schemes for Forward Backward Stochastic Differential Equations

Xu Wang & Weidong Zhao

Adv. Appl. Math. Mech., 15 (2023), pp. 737-768.

Published online: 2023-02

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  • Abstract

In this work, by combining the multistep discretization in time and the Sinc quadrature rule for approximating the conditional mathematical expectations, we will propose new fully discrete multistep schemes called “Sinc-multistep schemes” for forward backward stochastic differential equations (FBSDEs). The schemes avoid spatial interpolations and admit high order of convergence. The stability and the $K$-th order error estimates in time for the $K$-step Sinc multistep schemes are theoretically proved $(1≤K≤6).$ This seems to be the first time for analyzing fully time-space discrete multistep schemes for FBSDEs. Numerical examples are also presented to demonstrate the effectiveness, stability, and high order of convergence of the proposed schemes.

  • AMS Subject Headings

65C30, 60H10, 60H35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-15-737, author = {Wang , Xu and Zhao , Weidong}, title = {Sinc-Multistep Schemes for Forward Backward Stochastic Differential Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2023}, volume = {15}, number = {3}, pages = {737--768}, abstract = {

In this work, by combining the multistep discretization in time and the Sinc quadrature rule for approximating the conditional mathematical expectations, we will propose new fully discrete multistep schemes called “Sinc-multistep schemes” for forward backward stochastic differential equations (FBSDEs). The schemes avoid spatial interpolations and admit high order of convergence. The stability and the $K$-th order error estimates in time for the $K$-step Sinc multistep schemes are theoretically proved $(1≤K≤6).$ This seems to be the first time for analyzing fully time-space discrete multistep schemes for FBSDEs. Numerical examples are also presented to demonstrate the effectiveness, stability, and high order of convergence of the proposed schemes.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0073}, url = {http://global-sci.org/intro/article_detail/aamm/21448.html} }
TY - JOUR T1 - Sinc-Multistep Schemes for Forward Backward Stochastic Differential Equations AU - Wang , Xu AU - Zhao , Weidong JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 737 EP - 768 PY - 2023 DA - 2023/02 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2022-0073 UR - https://global-sci.org/intro/article_detail/aamm/21448.html KW - Forward backward stochastic differential equations, multistep schemes, Sinc quadrature rule, error estimates. AB -

In this work, by combining the multistep discretization in time and the Sinc quadrature rule for approximating the conditional mathematical expectations, we will propose new fully discrete multistep schemes called “Sinc-multistep schemes” for forward backward stochastic differential equations (FBSDEs). The schemes avoid spatial interpolations and admit high order of convergence. The stability and the $K$-th order error estimates in time for the $K$-step Sinc multistep schemes are theoretically proved $(1≤K≤6).$ This seems to be the first time for analyzing fully time-space discrete multistep schemes for FBSDEs. Numerical examples are also presented to demonstrate the effectiveness, stability, and high order of convergence of the proposed schemes.

Xu Wang & Weidong Zhao. (2023). Sinc-Multistep Schemes for Forward Backward Stochastic Differential Equations. Advances in Applied Mathematics and Mechanics. 15 (3). 737-768. doi:10.4208/aamm.OA-2022-0073
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