So how can a drunkard walking down the street lead to such a scary sounding thing like ‘Stochastic Calculus‘? Under certain conditions and taking the continuous limit, the Drunkard’s Walk becomes Brownian Motion. I’ll try to show you how this all happens using a little bit of JavaScript. In the Drunkard’s Walk, we assumed that with each step the drunkard takes he moves a distance of 1 foot to either the left or right. Its natural to wonder if something interesting would happen if we scaled this distance and took many more steps. As a matter of fact, something interesting does happen!
Read the rest of this entry »
In 1827, the botanist Robert Brown was studying pollen particles as they floated in water. When viewed through a microscope, he observed that the particles seemed to move around as if the were alive. Although he couldn’t have known at the time, the seemingly random motion was caused by the collision of water molecules against the pollen particle. Later on, the random motion he observed would be given the name ‘Brownian Motion’.
Read the rest of this entry »