Strong rate of convergence for the Euler-Maruyama scheme of additive fractional SDEs with Lipschitz drift

Abstract

We study the strong convergence rate of the Euler-Maruyama scheme for additive stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H \in (0,1)$. Assuming the drift coefficient to be Lipschitz continuous, we show that the rate is $1$ if $H \in (1/2,1)$, and $1/2+H-\varepsilon$, for any $\varepsilon>0$, if $H \in (0,1/2]$. The main ingredient is a shifted stochastic sewing argument, which exploits the conditional Gaussian structure of fractional Brownian motion to control the noise discretization error.

Disclosure

“1];Rd ) ∥Lp ≤ C0 n−1 , where [·]C 1/4 ([0,1];Rd ) denotes the usual Hölder seminorm. In particular, sup |Xt − Xtn | ≤ C0 n−1 . t∈[0,1] Lp Declaration of generative AI and AI-assisted technologies in the writ- ing process The author used ChatGPT for translation, proofreading, and language edit- ing. The author reviewed and edited the content and takes full responsibility for the article. Data availa”

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2026-08-23T19:08:07.981464Z

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