# Functional Limit Theorems

Chapter
Part of the Springer Series in Operations Research and Financial Engineering book series (ORFE)

## Abstract

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 o, 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.

## Keywords

Passage Time Invariance Principle Iterate Logarithm Functional Central Limit Theorem Uniform Topology
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