Brownian rough path small-ball positivity
= Brownian rough path small-ball positivity
{c}
{title2=$\mathbb P(d_p(\mathbf B,e)<\varepsilon)>0$}
For every $2<p<3$ and every positive radius, the canonical Brownian enhancement has positive probability of lying in the displayed <rough path metric> ball. This controls both displacement and area. Together with <Cameron-Martin quasi-invariance of enhanced Brownian motion>, it puts every lifted Cameron-Martin control in the <support of enhanced Brownian motion>.