The idea of this post is to show how Donsker’s Theorem (also known as Donsker’s Invariance Principle, or the Functional Central Limit Theorem) allows us to simulate paths of the one-dimensional standard Brownian motion using different kinds of random walks.
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A very brief recollection of the history of the Central Limit Theorem: 162 years from Moivre to Feller in a page. If you are interested in reading more about the history of the Central Limit Theorem, I highly recommend: The Central Limit Theorem Around 1935 paper by L. Le Cam published in 1986 in Statistical Science. A History of the Central Limit Theorem, From Classical to Modern Theory Probability book by Hans Fischer published in 2011 […]
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