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.
Publié le : 1981-04-14
Classification:
Central limit theorem,
random walk,
Wiener Tauberian theory,
number-theoretic density,
Borel summability,
60F05,
60J15,
40E05
@article{1176994464,
author = {Bingham, N. H.},
title = {Tauberian Theorems and the Central Limit Theorem},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 221-231},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994464}
}
Bingham, N. H. Tauberian Theorems and the Central Limit Theorem. Ann. Probab., Tome 9 (1981) no. 6, pp. 221-231. http://gdmltest.u-ga.fr/item/1176994464/