Abstract
This paper concerns the strong convergence rate of an averaging principle for two-time-scale coupled forward–backward stochastic differential equations (CFBSDEs, for short) driven by fractional Brownian motion (fBm, for short). The fast component is a forward stochastic differential equation (FSDE, for short) driven by Brownian motion, while the slow component is a backward stochastic differential equation (BSDE, for short) driven by fBm with the Hurst index greater than 1/2. Combining Malliavin calculus theory with stochastic integral and Khasminskii’s time discretization method, the rate of strong convergence for the slow component towards the solution of the averaging equation in the mean square sense is derived. The strong convergence rate of an averaging principle for fast–slow CFBSDEs driven by fBm is new.
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Acknowledgements
The first author acknowledges Professor **qiao Duan careful reading of manuscript, correcting errors, detailed comments and valuable suggestions, which improve the quality of this paper. The first author also thanks the support provided by NSFs of China No.11971154.
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Xu, J., Lian, Q. & Wu, JL. A Strong Averaging Principle Rate for Two-Time-Scale Coupled Forward–Backward Stochastic Differential Equations Driven by Fractional Brownian Motion. Appl Math Optim 88, 32 (2023). https://doi.org/10.1007/s00245-023-10008-2
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DOI: https://doi.org/10.1007/s00245-023-10008-2
Keywords
- Stochastic averaging principle
- Convergence rate
- Fractional Brownian motion
- Fast–slow forward–backward stochastic differential equations