Brownian Hölder regularity
= Brownian Hölder regularity
{c}
On every compact time interval, a Brownian path is almost surely a <Hölder continuous function> of every exponent $\alpha<1/2$, and of no exponent $\alpha\geq1/2$. In particular, $B_t=o(t^\gamma)$ as $t\downarrow0$ for every $\gamma<1/2$ after choosing a Hölder exponent strictly between $\gamma$ and $1/2$.