Let $W$ be a standard $d$-dimensional Brownian motion. For each $N \geq 1$ let $W^N$ be the piecewise linear interpolation of $W$ along the uniform partition $\mathcal{D}_N = \{0 = t_0 < t_1 < \cdots < t_N = T\}$ with step size $h = T/N$. Then there exists a random geometric $p$-rough path $W$, with $p \in (2,3)$, such that for $\mathbb{P}$-almost every $\omega \in \Omega$, \begin{align*} \rho_{p,T}\bigl(S^2(W^N)(\omega),\, W(\omega)\bigr) \to 0 \quad \text{as } N \to \infty, \end{align*} and \begin{align*} W(\omega)_{s,t} = \left(1,\; (W_t - W_s)(\omega),\; \left(\int_s^t (W_u - W_s) \otimes \circ\, dW_u\right)(\omega)\right), \end{align*} where the stochastic integral is in the Stratonovich sense. The object $W$ is called the **Stratonovich enhanced Brownian motion**. (Friz–Victoir 2010, Corollary 13.22)