Open Access
Fall and Winter 2017 A new direct proof of the central limit theorem
Vladimir Dobrić, Patricia Garmirian
Illinois J. Math. 61(3-4): 355-370 (Fall and Winter 2017). DOI: 10.1215/ijm/1534924830

Abstract

We prove the central limit theorem from the definition of weak convergence using the Haar basis, calculus, and elementary probability, and we estimate the rate of convergence off the tails. The use of the Haar basis pinpoints the role of $L^{2}([0,1])$ in the CLT as well as the assumption of finite variance.

Citation

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Vladimir Dobrić. Patricia Garmirian. "A new direct proof of the central limit theorem." Illinois J. Math. 61 (3-4) 355 - 370, Fall and Winter 2017. https://doi.org/10.1215/ijm/1534924830

Information

Received: 18 January 2017; Revised: 26 February 2018; Published: Fall and Winter 2017
First available in Project Euclid: 22 August 2018

zbMATH: 06932507
MathSciNet: MR3845724
Digital Object Identifier: 10.1215/ijm/1534924830

Subjects:
Primary: 60F05
Secondary: 28A33 , ‎42C40

Rights: Copyright © 2017 University of Illinois at Urbana-Champaign

Vol.61 • No. 3-4 • Fall and Winter 2017
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