PreprintCC BY-NC-ND 4.0arXiv
Strong convergence of Euler-Maruyama schemes for 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∈(0,1). Assuming the drift coefficient to be Lipschitz continuous, we establish strong convergence bounds of order $1$ 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.
Versions
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BibTeX
@misc{moritoki2026strong,
title = {{Strong convergence of Euler-Maruyama schemes for additive fractional SDEs with Lipschitz drift}},
author = {Tsukasa Moritoki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.24166},
eprint = {2607.24166},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.24166},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Strong convergence of Euler-Maruyama schemes for additive fractional SDEs with Lipschitz drift
AU - Tsukasa Moritoki
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2607.24166
UR - https://arxiv.org/abs/2607.24166
AB - 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 establish strong convergence bounds of order $1$ 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.
ER -