Optimal Error Estimates for a Fully Discrete Euler Scheme for Decoupled Forward Backward Stochastic Differential Equations

AbstractIn error estimates of various numerical approaches for solving decoupled forward backward stochastic differential equations (FBSDEs), the rate of convergence for one variable is usually less than for the other. Under slightly strengthened smoothness assumptions, we show that the fully discrete Euler scheme admits a first-order rate of convergence for both variables.

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Optimal Error Estimates of Two Mixed Finite Element Methods for Parabolic Integro-Differential Equations with Nonsmooth Initial Data

Journal of Scientific Computing ◽

10.1007/s10915-012-9666-8 ◽

2013 ◽

Vol 56 (1) ◽

pp. 131-164 ◽

Cited By ~ 9

Author(s):

Deepjyoti Goswami ◽

Amiya K. Pani ◽

Sangita Yadav

Keyword(s):

Finite Element ◽

Initial Data ◽

Differential Equations ◽

Error Estimates ◽

Finite Element Methods ◽

Mixed Finite Element ◽

Mixed Finite Element Methods ◽

Optimal Error Estimates ◽

Optimal Error ◽

Nonsmooth Initial Data

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A Fully Discrete Explicit Multistep Scheme for Solving Coupled Forward Backward Stochastic Differential Equations

Advances in Applied Mathematics and Mechanics ◽

10.4208/nmtma.oa-2019-0199 ◽

2020 ◽

Vol 12 (3) ◽

pp. 643-663

Author(s):

Ying Liu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Backward Stochastic Differential Equations ◽

Fully Discrete ◽

Multistep Scheme

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Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation

Journal of Scientific Computing ◽

10.1007/s10915-008-9247-z ◽

2008 ◽

Vol 40 (1-3) ◽

pp. 257-272 ◽

Cited By ~ 47

Author(s):

Marcus J. Grote ◽

Dominik Schötzau

Keyword(s):

Wave Equation ◽

Error Estimates ◽

Optimal Error Estimates ◽

Optimal Error ◽

Interior Penalty ◽

Fully Discrete ◽

Dg Method

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Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations

Bernoulli ◽

10.3150/bj/1161614951 ◽

2006 ◽

Vol 12 (5) ◽

pp. 889-916 ◽

Cited By ~ 83

Author(s):

Jean-Philippe Lemor ◽

Emmanuel Gobet ◽

Xavier Warin

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Rate Of Convergence ◽

Backward Stochastic Differential Equations ◽

Regression Method

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Optimal Error Estimates of Spectral Petrov--Galerkin and Collocation Methods for Initial Value Problems of Fractional Differential Equations

SIAM Journal on Numerical Analysis ◽

10.1137/140988218 ◽

2015 ◽

Vol 53 (4) ◽

pp. 2074-2096 ◽

Cited By ~ 24

Author(s):

Zhongqiang Zhang ◽

Fanhai Zeng ◽

George Em Karniadakis

Keyword(s):

Differential Equations ◽

Error Estimates ◽

Fractional Differential Equations ◽

Initial Value Problems ◽

Collocation Methods ◽

Optimal Error Estimates ◽

Initial Value ◽

Optimal Error ◽

Fractional Differential ◽

Galerkin And Collocation Methods

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A Fully Discrete Explicit Multistep Scheme for Solving Coupled Forward Backward Stochastic Differential Equations

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.oa-2019-0079 ◽

2020 ◽

Vol 12 (3) ◽

pp. 643-663

Author(s):

Ying Liu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Backward Stochastic Differential Equations ◽

Fully Discrete ◽

Multistep Scheme

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A Numerical Method and its Error Estimates for the Decoupled Forward-Backward Stochastic Differential Equations

Communications in Computational Physics ◽

10.4208/cicp.280113.190813a ◽

2014 ◽

Vol 15 (3) ◽

pp. 618-646 ◽

Cited By ~ 14

Author(s):

Weidong Zhao ◽

Wei Zhang ◽

Lili Ju

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Numerical Method ◽

Error Estimates ◽

Backward Stochastic Differential Equations ◽

Second Order ◽

Numerical Schemes ◽

Reference Equations ◽

Taylor Scheme ◽

Theoretical Results

AbstractIn this paper, a new numerical method for solving the decoupled forward-backward stochastic differential equations (FBSDEs) is proposed based on some specially derived reference equations. We rigorously analyze errors of the proposed method under general situations. Then we present error estimates for each of the specific cases when some classical numerical schemes for solving the forward SDE are taken in the method; in particular, we prove that the proposed method is second-order accurate if used together with the order-2.0 weak Taylor scheme for the SDE. Some examples are also given to numerically demonstrate the accuracy of the proposed method and verify the theoretical results.

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