Abstract
The functional central limit theorem, or invariance principle, refers to convergence in distribution of centered and rescaled random walks having finite second moments to Brownian motion. This provides a tool for computing asymptotic limits of functionals of rescaled random walks by analyzing the corresponding functional of Brownian motion. The term “invariance principle”refers to the invariance of the distribution of the limit, namely Brownian motion, regardless of the specific random walk increments, with a finite second moment. The proof given here is by a beautiful technique of Skorokhod in which the random walk paths are embedded within the Brownian motion.
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