Tauberian Theorems and the Central Limit Theorem
Copyright policy )Tauberian Theorems and the Central Limit Theorem
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.
Abel, Borel and power series methods, Tauberian theorems for random walks, 40E05, Tauberian theorems, Central limit theorem, Borel summability, central limit theorem, number- theoretic densities, Wiener Tauberian theory, Central limit and other weak theorems, number-theoretic density, random walk, 60F05, 60J15
Abel, Borel and power series methods, Tauberian theorems for random walks, 40E05, Tauberian theorems, Central limit theorem, Borel summability, central limit theorem, number- theoretic densities, Wiener Tauberian theory, Central limit and other weak theorems, number-theoretic density, random walk, 60F05, 60J15
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