How can we compute the probability that Brownian motion hits $b$ before $a$?
Thanks.
2026-03-26 17:51:37.1774547497
Hitting time Brownian motion
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Brownian motion is a martingale so you can apply the Optional stopping theorem. If $t$ is the first hitting time of $a$ or $b$, then, $$ 0 = \mathbb{E}[X_0] = \mathbb{E}[X_t] = ap_a + bp_b $$ Can you finish it now?