In this paper, we study the asymptotic behavior of multi-scale stochastic differential equations driven by fractional Brownian noise and standard Brownian motion. The fast component is driven by a Brownian motion, while the slow component is driven by a fractional Brownian motion with Hurst parameter H(H∈(12,1)). We study the regularity estimates for the solution to the Poisson equation to derive the optimal strong convergence order 1/2−ε∗ (ε∗ is small enough).
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Lv et al. (2026) studied this question.
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