Brownian Motion and the Calculus of Randomness by Lola Kovalski ’25 & Jacob Cohen ’25

Brownian Motion and the Calculus of Randomness by Lola Kovalski ’25 & Jacob Cohen ’25, Wednesday September 18, 1:00 – 1:50pm, North Science Building 113, Wachenheim, Mathematics Colloquium

Abstract:

From stocks to particles, many real-world objects continuously move in seemingly random directions. The way this is mathematically modeled is via Brownian motion, the subject of this talk. We first build intuition by extending a discrete time random walk to a continuous time stochastic process. Following that, we formally define Brownian motion and the properties of its paths. Finally, we prove that with probability one, Brownian motion is nowhere differentiable, thereby motivating the need for a new type of calculus to apply to stochastic processes.