Wilfrid Kendall notes on the complexity of the paths of Brownian motion: If you run Brownian motion in two dimensions for a positive amount of time, it will write your name. The oddness and complexity of Brownian motion reveal a really deep subject in the field of mathematics that cannot be fully understood and explained even until now. The purpose of this paper is to introduce the Brownian motion with its properties and to explain how it is applied in an everyday but totally unpredictable environment like the stock market.
Ermogenous, Angeliki, "Brownian Motion and Its Applications In The Stock Market" (2006). Undergraduate Mathematics Day, Electronic Proceedings. 15.