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April, 1981 Tauberian Theorems and the Central Limit Theorem
N. H. Bingham
Ann. Probab. 9(2): 221-231 (April, 1981). DOI: 10.1214/aop/1176994464


We prove Tauberian theorems for random walks with positive drift obeying the central limit theorem. The results include (i) conclusions involving certain averages, relevant to number-theoretic densities and extending results of Diaconis and Stein; (ii) pointwise conclusions, including the classical Borel-Tauber theorem and extending results of Schmaal, Stam and de Vries.


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N. H. Bingham. "Tauberian Theorems and the Central Limit Theorem." Ann. Probab. 9 (2) 221 - 231, April, 1981.


Published: April, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0459.60021
MathSciNet: MR606985
Digital Object Identifier: 10.1214/aop/1176994464

Primary: 60F05
Secondary: 40E05 , 60J15

Keywords: Borel summability , central limit theorem , number-theoretic density , Random walk , Wiener Tauberian theory

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 2 • April, 1981
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