Functional Limit Theorems
The classical central limit theorem was generalized to a functional central limit theorem by Donsker (1951) (see Theorem A.3.2). In words the result means that one considers the partial sums S 0,S 1,...,S n of i.i.d. variables jointly for each n and shows that if the mean and variance are finite then the (polygonal) process obtained by normalization (and linear interpolation), behaves, asymptotically, like Brownian motion.
KeywordsRandom Walk Passage Time Iterate Logarithm Functional Central Limit Theorem Positive Jump
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