Details of Research Outputs

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.