Tauberian Theorems and the Central Limit Theorem

Author:
  • NBN. H. Bingham
    N. H. Bingham
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Abstract
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.