Infinite-horizon crossing probability for Brownian motion with negative drift
= Infinite-horizon crossing probability for Brownian motion with negative drift
For $a,y>0$,
$$
\mathbb P\!\left(\sup_{u\geq0}(W_u-au)>y\right)=e^{-2ay}.
$$
= Infinite-horizon crossing probability for Brownian motion with negative drift
For $a,y>0$,
$$
\mathbb P\!\left(\sup_{u\geq0}(W_u-au)>y\right)=e^{-2ay}.
$$