If X is standard Brownian motion, what is the distribution of its absolute maximum |X|t∗ = sups ≤ t|Xs| over a time interval [0, t]? Previously, I looked at how the reflection principle can be used to determine that the maximum Xt∗ = sups ≤ tXs has the same distribution as |Xt|. This is not the same thing as the maximum of the absolute … Continue reading The Minimum and Maximum of Brownian motion