Brownian Motions and Quantifying Randomness in Physical Systems
ergospherical
Stochastic calculus has come a long way since Robert Brown described the motion of pollen through a microscope in 1827. It’s now a key player in data science, quant finance, and mathematical biology. This article is drawn from notes I wrote for an undergraduate statistical physics course a few months ago. There won’t be any mathematical rigor.
Table of Contents
In 1d, the term Brownian motion is reserved for continuous functions ##W(t)## that satisfy three key conditions:
- The motion starts at.