59.1 Bachelier's Principle
Bachelier's principle: the running maximum of 1-dimensional Brownian motion has the same endpoint distribution as the absolute value of Brownian motion. This can be used to compute the probability density of the hitting time of any height, and from there other interesting statistics (like the last hitting time of 0 in a fixed compact interval) can be computed as well. 1-dimensional Brownian motion is null-recurrent.