Brownian Motion

Brownian motion owes its name to the botanist Robert Brown who observed the chaotic motion of pollen grains in a liquid. From the mathematical point of view, it received attention from Albert Einstein and Louis Bachelier. The latter was motivated by his interest in finance, finding that the model could serve to describe the fluctuations of the stock market, and nowadays, its role in mathematical finance is well established. Brownian motion is also called the Wiener process, after Norbert Wiener, who introduced it in the theory of stochastic systems driven by white noise, a notion that we shall discuss in the next chapter.