Functional Limit Theorems

  • Allan Gut
Part of the Applied Probability book series (APPLIEDPROB, volume 5)


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.


Random Walk Passage Time Iterate Logarithm Functional Central Limit Theorem Positive Jump 
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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • Allan Gut
    • 1
  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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