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A strong averaging principle rate for two-time-scale coupled forward-backward stochastic differential equations driven by fractional Brownian motion

Jie Xu, Qiqi Lian, Jiang-lun Wu

Applied Mathematics and Optimization, Volume: 88, Issue: 32

Swansea University Author: Jiang-lun Wu

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DOI (Published version): 10.1007/s00245-023-10008-2

Abstract

This paper concerns the strong convergence rate of an averaging principle for two- time-scale forward-backward stochastic differential equations (FBSDEs, for short) driven by fractional Brownian motion (fBm, for short). The fast component is driven by Brownian motion, while the slow component is dri...

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Published in: Applied Mathematics and Optimization
ISSN: 0095-4616 1432-0606
Published: Springer
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URI: https://cronfa.swan.ac.uk/Record/cronfa63257
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Abstract: This paper concerns the strong convergence rate of an averaging principle for two- time-scale forward-backward stochastic differential equations (FBSDEs, for short) driven by fractional Brownian motion (fBm, for short). The fast component is driven by Brownian motion, while the slow component is driven by fBm with the Hurst index greater than 1/2. Combining Malliavin calculus theory to 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 averaging principle for fast-slow FBSDEs driven by fBm is new.
Keywords: Stochastic averaging principle, Convergence rate, Fractional Brownian motion, Fast–slow forward–backward stochastic differential equations
College: Faculty of Science and Engineering
Issue: 32

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