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

2026/07/27 by Tsukasa Moritoki
#math.PR

paper · pdf

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 ∈ (0,1). Assuming the drift coefficient to be Lipschitz continuous, we show that the rate is 1 if H ∈ (1/2,1), and 1/2+H-ε, for any ε>0, if H ∈ (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.

Citations

• Regularization by regular noise: a numerical result
• Strong convergence rate of the Euler scheme for SDEs driven by additive rough fractional noises

Related

• Strong convergence rate of the Euler scheme for SDEs driven by additive rough fractional noises
• Strong rate of convergence of the Euler scheme for SDEs with irregular drift driven by Levy noise
• The Euler-Maruyama method for SDEs with low-regularity drift
• Convergence Rate of the Euler-Maruyama Scheme Applied to Diffusion Processes with L Q -- L ρ Drift Coefficient and Additive Noise
• Convergence rate of the Euler-Maruyama scheme to density dependent SDEs driven by α-stable additive noise