How can one compute $P(\sup_{0\leq s\leq t} (c_1X_1(s) - c_2X_2(s))>x)$, where $x>0$, $c_1, c_2$ are two fixed constants and $X_i$'s are Brownian motions with a drift, i.e. $X_i(t) = \mu_it+\sigma B_i(t)$, $i =1,2$, and $B_1(t)$ and $B_2(t)$ are independent standard Brownian motions? This is just a problem from my studying packet for my exam. Thank you in advance for any help!
2026-04-29 08:42:13.1777452133
Supremum of the difference of two Brownian motion with a drift
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