Result: Some Tauberian Theorems Related to Coin Tossing: Some Tauberian theorems related to coin tossing

Title:
Some Tauberian Theorems Related to Coin Tossing: Some Tauberian theorems related to coin tossing
Authors:
Diaconis, Persi, Stein, Charles
Source:
Ann. Probab. 6, no. 3 (1978), 483-490
Publisher Information:
Institute of Mathematical Statistics, 1978.
Publication Year:
1978
Subject Terms:
Probabilistic theory: distribution modulo \(1\), metric theory of algorithms, Combinatorial probability, Tauberian theorems, 40G05, summability, Probabilistic number theory, 01 natural sciences, Euler Density, Cesaro Density, Cesàro, Euler, Nörlund and Hausdorff methods, Special sequences and polynomials, 0101 mathematics, Tauberian Theorems, 66C05
Document Type:
Academic journal Article<br />Other literature type
File Description:
application/xml; application/pdf
ISSN:
0091-1798
DOI:
10.1214/aop/1176995532
Access URL:
https://www.jstor.org/stable/pdfplus/2243150.pdf
https://projecteuclid.org/journals/annals-of-probability/volume-6/issue-3/Some-Tauberian-Theorems-Related-to-Coin-Tossing/10.1214/aop/1176995532.full
https://projecteuclid.org/download/pdf_1/euclid.aop/1176995532
https://projecteuclid.org/euclid.aop/1176995532
https://statweb.stanford.edu/~cgates/PERSI/papers/tauberian78.pdf
http://projecteuclid.org/download/pdf_1/euclid.aop/1176995532
http://projecteuclid.org/euclid.aop/1176995532
Rights:
implied-oa
Accession Number:
edsair.doi.dedup.....7c283d5a8ece8c4c0453a75cc0b18d6f
Database:
OpenAIRE

Further Information

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.