Understanding the geometric Brownian motion model
The name Brownian comes from the Scottish botanist Robert Brown who, in 1827, observed, under the microscope, how pollen particles suspended in water moved continuously in a random and unpredictable way. In 1905, it was Einstein who gave a molecular interpretation of the phenomenon of movement observed by Brown. He suggested that the motion of the particles was mathematically describable, assuming that the various jumps were due to the random collisions of pollen particles with water molecules.
Today, Brownian motion is, above all, a mathematical tool in the context of probability theory. This mathematical theory has been used to describe an ever-widening set of phenomena, studied by disciplines that are very different from physics. For instance, the prices of financial securities, the spread of heat, animal populations, bacteria, illness, sound, and light are modeled using the same instrument.