Mean-square convergence of numerical approximations for
a class of backward stochastic differential equations

AbstractIn this paper, we investigate the mean-square convergence of the split-step θ-scheme for nonlinear stochastic differential equations with jumps. Under some standard assumptions, we rigorously prove that the strong rate of convergence of the split-step θ-scheme in strong sense is one half. Some numerical experiments are carried out to assert our theoretical result.

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Mean-square numerical approximations to random periodic solutions of stochastic differential equations

Advances in Difference Equations ◽

10.1186/s13662-015-0626-0 ◽

2015 ◽

Vol 2015 (1) ◽

Cited By ~ 5

Author(s):

Qingyi Zhan

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Periodic Solutions ◽

Mean Square ◽

Numerical Approximations

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On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations

Journal of Scientific Computing ◽

10.1007/s10915-018-00903-0 ◽

2019 ◽

Vol 79 (3) ◽

pp. 1534-1571 ◽

Cited By ~ 8

Author(s):

Weinan E ◽

Martin Hutzenthaler ◽

Arnulf Jentzen ◽

Thomas Kruse

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Backward Stochastic Differential Equations ◽

High Dimensional ◽

Parabolic Partial Differential Equations ◽

Numerical Approximations ◽

Partial Differential ◽

Nonlinear Parabolic

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Mean square convergence of explicit two-step methods for highly nonlinear stochastic differential equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2019.05.037 ◽

2019 ◽

Vol 361 ◽

pp. 466-483 ◽

Cited By ~ 1

Author(s):

Jingjun Zhao ◽

Yulian Yi ◽

Yang Xu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Mean Square ◽

Nonlinear Stochastic Differential Equations ◽

Highly Nonlinear ◽

Mean Square Convergence

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Averaging Principle for Backward Stochastic Differential Equations

Discrete Dynamics in Nature and Society ◽

10.1155/2021/6615989 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Yuanyuan Jing ◽

Zhi Li

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Stochastic Systems ◽

Backward Stochastic Differential Equations ◽

Averaging Principle ◽

Mean Square ◽

The One

The averaging principle for BSDEs and one-barrier RBSDEs, with Lipschitz coefficients, is investigated. An averaged BSDEs for the original BSDEs is proposed, as well as the one-barrier RBSDEs, and their solutions are quantitatively compared. Under some appropriate assumptions, the solutions to original systems can be approximated by the solutions to averaged stochastic systems in the sense of mean square.

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