In this note we construct solutions to rough differential equations ${\rm d} Y = f(Y) \,{\rm d} X$ with a driver $X \in C^\alpha([0,T];\mathbb{R}^d)$, $\frac13 < \alpha \le \frac12$, using a splitting-up scheme. We show convergence of our scheme to solutions in the sense of Davie by a new argument and give a rate of convergence.

翻译：本文通过分裂法构造了粗糙微分方程 ${\rm d} Y = f(Y) \,{\rm d} X$ 的解，其中驱动项 $X \in C^\alpha([0,T];\mathbb{R}^d)$，且 $\frac13 < \alpha \le \frac12$。我们通过一种新的论证方法证明了该格式在 Davie 意义下收敛于解，并给出了收敛速率。