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A Strong Convergence Rate of the Averaging Principle for Two-Time-Scale Forward-Backward Stochastic Differential Equations

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Abstract

In this paper, we study the strong convergence rate of the averaging principle of two-time-scale forward-backward stochastic differential equations (FBSDEs, for short). First, we present the well-posedness of the objective equations and then we give some a priori estimates for FBSDEs, backward stochastic auxiliary equations and backward stochastic averaged equations. Second, a strong convergence rate of the averaging principle for two-time-scale FBSDEs is derived. As far as we know, this is the first result on the strong convergence rate of the averaging principle of two-time-scale backward stochastic differential equations (BSDEs, for short).

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All data, models, and code generated or used during the study appear in the submitted article.

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Acknowledgements

The authors would like to thank the anonymous referee for his/her valuable suggestions and remarks.

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  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, Henan, People’s Republic of China

    Jie Xu & Qiqi Lian

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  1. Jie Xu
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  2. Qiqi Lian
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Correspondence to Jie Xu.

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Xu, J., Lian, Q. A Strong Convergence Rate of the Averaging Principle for Two-Time-Scale Forward-Backward Stochastic Differential Equations. J Theor Probab 36, 2590–2610 (2023). https://doi.org/10.1007/s10959-023-01278-1

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  • DOI: https://doi.org/10.1007/s10959-023-01278-1

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