Enhanced Brownian motion
= Enhanced Brownian motion
{title2=$\mathbf B_{s,t}=(1,B_t-B_s,\int_s^t(B_r-B_s)\otimes\circ dB_r)$}
The Stratonovich enhancement of <Brownian motion> is a geometric $p$-rough path for every $p>2$. Its second level consists of <Lévy area> and the prescribed symmetric tensor. Its increments satisfy the <Chen identity> and have finite Hölder rough-path norms at every exponent below $1/2$.