Tauberian theorems and the central limit theorem

DOI10.1214/AOP/1176994464zbMath0459.60021OpenAlexW2021969203MaRDI QIDQ1152161

Nicholas H. Bingham

Publication date: 1981

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176994464

zbMATH Keywords

central limit theoremnumber- theoretic densitiesTauberian theorems for random walks

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Abel, Borel and power series methods (40G10) Tauberian theorems (40E05)

Related Items (18)

Riesz and Valiron means and fractional moments ⋮ Riesz means and self-neglecting functions ⋮ Non-uniform rates of convergence for double arrays of independent random variables with applications ⋮ Limit theorems for methods of summation of independent random variables. II ⋮ Statistical gap Tauberian theorems in metric spaces ⋮ Tauberian Korevaar ⋮ Probabilistic and Deterministic Averaging ⋮ Tauberian theorems for Jakimovski and Karamata‐Stirling methods ⋮ The central limit theorem for summability methods of I.I.D. random variables ⋮ Summability methods and almost sure convergence ⋮ On Valiron and circle convergence ⋮ General regular variation, Popa groups and quantifier weakening ⋮ Statistical extensions of some classical Tauberian theorems ⋮ Logarithmic moving averages ⋮ Tauberian theorems via statistical convergence ⋮ Extremes and regular variation ⋮ Abelian, Tauberian, and Mercerian theorems for arithmetic sums. ⋮ Weighted versions of Beurling's Tauberian theorem

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