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

Jie Xu () and Qiqi Lian
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Jie Xu: Henan Normal University
Qiqi Lian: Henan Normal University

Journal of Theoretical Probability, 2023, vol. 36, issue 4, 2590-2610

Abstract: 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).

Keywords: Stochastic averaging principle; Convergence rate; Fast–slow FBSDEs; 60H10; 70K65; 70K70 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-023-01278-1

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