The original Donsker theorem says that a standard random walk converges in distribution to a Brownian motion in the space of continuous functions. It has recently been extended to enriched random walks and enriched Brownian motion. We use the Stein-Dirichlet method to precise the rate of this convergence in the topology of fractional Sobolev spaces.

中文翻译：

---

斯坦因的粗糙路径方法

最初的Donsker定理说，在连续函数的空间中，标准随机游动在分布上收敛为布朗运动。最近，它已扩展到丰富的随机游走和丰富的布朗运动。我们使用Stein-Dirichlet方法来精确地计算分数Sobolev空间拓扑中的收敛速度。