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1 IEOR 4700: Notes on Brownian Motion - Columbia University

variance t. Similarly, using the stationary and independent increments property, we conclude that B(t)−B(s) has a normal distribution with mean 0 and variance t−s, and more generally: the limiting BM process is a process with continuous sample paths that has both stationary and independent normally distributed (Gaussian) increments: If t 0 ...

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