Brownian reflection at a stopping time
= Brownian reflection at a stopping time
{c}
Reflecting a <Brownian motion> $B$ after a <stopping time> $T$ by $\widehat B_t=2B_T-B_t$ for $t>T$, and leaving it unchanged for $t\leq T$, preserves its path <probability distribution>. For finite $T$, the <Strong Markov property> and symmetry of the future <Brownian motion> prove this. When $T=\infty$, the path is left unchanged.