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June, 1978 Some Tauberian Theorems Related to Coin Tossing
Persi Diaconis, Charles Stein
Ann. Probab. 6(3): 483-490 (June, 1978). DOI: 10.1214/aop/1176995532


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.


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Persi Diaconis. Charles Stein. "Some Tauberian Theorems Related to Coin Tossing." Ann. Probab. 6 (3) 483 - 490, June, 1978.


Published: June, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0396.10044
MathSciNet: MR474449
Digital Object Identifier: 10.1214/aop/1176995532

Primary: 66C05
Secondary: 40G05

Keywords: Probabilistic number theory , summability , Tauberian theorems

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 3 • June, 1978
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