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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Reinforced random walks and random distributions


Authors: R. Daniel Mauldin and S. C. Williams
Journal: Proc. Amer. Math. Soc. 110 (1990), 251-258
MSC: Primary 60A99; Secondary 60C05, 60G09, 62A15
MathSciNet review: 1012934
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Abstract: Consider a classical Polya urn process on a complete binary tree. This process generates an exchangeable sequence of random variables $ {Z_n}$, with values in $ [0,1]$. It is shown that the empirical distribution $ ^\char93 \{ i \leq n:{Z_i} \leq s\} /n$ converges weakly and the distribution of this limit is the same as a standard Dubins-Freedman random distribution. As an application, the variance of the first moment of these Dubins-Freedman distributions is calculated.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1012934-1
PII: S 0002-9939(1990)1012934-1
Keywords: Polya urn process, exchangable, empirical distribution, random distribution
Article copyright: © Copyright 1990 American Mathematical Society