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!
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Believe it or not, but a drunk walking down the street is the basis for Stochastic Calculus. The sloppy walking motion of a drunk leads to some interesting models, some of the most complex of which are used to model financial derivatives.
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