Functional Limit Theorems

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


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.


Passage Time Invariance Principle Iterate Logarithm Functional Central Limit Theorem Uniform Topology 
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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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