Let $A$ be a subset of the integers and let $S_n$ be the number of heads in $n$ tosses of a $p$ coin. If $\lim_{n\rightarrow\infty} P(S_n \in A)$ exists for some $p$ then the limit exists for all $p$ and does not depend on $p$. The relation of the limit to the density of $A$ and to a similar Poisson limit is also given.
Publié le : 1978-06-14
Classification:
Probabilistic number theory,
Tauberian theorems,
summability,
66C05,
40G05
@article{1176995532,
author = {Diaconis, Persi and Stein, Charles},
title = {Some Tauberian Theorems Related to Coin Tossing},
journal = {Ann. Probab.},
volume = {6},
number = {6},
year = {1978},
pages = { 483-490},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995532}
}
Diaconis, Persi; Stein, Charles. Some Tauberian Theorems Related to Coin Tossing. Ann. Probab., Tome 6 (1978) no. 6, pp. 483-490. http://gdmltest.u-ga.fr/item/1176995532/