I was wondering if there exist a known distribution function or a nice closed form describing the first hitting time to a given threshold $a$, $T_a$, for a Brownian motion bounded by a upper reflecting barrier at $b$, with $a<b$ and starting from an initial value $c$, $a<c<b$. Any hints, reference, or suggestion is appreciated.
2026-03-30 00:04:44.1774829084
Hitting time for Brownian motion with upper reflecting boundary
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