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Maximal Percentages in Pólya's Urn

Part of: Combinatorial probability

Published online by Cambridge University Press:  30 January 2018

Ernst Schulte-Geers  and
Wolfgang Stadje
Ernst Schulte-Geers*
Affiliation:
Bundesamt für Sicherheit in der Informationstechnik
Wolfgang Stadje*
Affiliation:
University of Osnabrück
*
∗ Postal address: Bundesamt für Sicherheit in der Informationstechnik (BSI), Godesberger Allee 185-189, 53175 Bonn, Germany. Email address: ernst.schulte-geers@bsi.bund.de
∗∗ Postal address: Institute of Mathematics, University of Osnabrück, 49069 Osnabrück, Germany. Email address: wstadje@uos.de
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Abstract

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We show that the supremum of the successive percentages of red balls in Pólya's urn model is almost surely rational, give the set of values that are taken with positive probability, and derive several exact distributional results for the all-time maximal percentage.

Keywords

Pólya's urnbinomial random walkall-time maximal percentageexact distribution

MSC classification

Primary: 60C05: Combinatorial probability
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 1 , March 2015 , pp. 180 - 190
Copyright
© Applied Probability Trust 

References

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