Let $B_t$, $M_t$, and $m_t$ be a standard Brownian motion and its running maximum and minimum, respectively. The joint distribution $(B_t, M_t)$, and hence by symmetry $(B_t, m_t)$, is well-known. Is there an equally easy closed form for the CDF of $(M_t, m_t)$?
2026-04-19 02:11:17.1776564677
Joint distribution of running max and min of a standard Brownian motion
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