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The Brownian motion is one of the most interesting and useful of all Stochastic Processes. It has an enormous range of applications ranging from physics (Einstein) to finance (starting with Bachelier). In this talk we will define and prove the existence of the Brownian motion, by showing that it can be represented as the random sum of integrals of orthogonal functions.
The material for this talk is taken from Michael Steele's textbook: Stochastic Calculus and Financial Applications (chapter 3).
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