Reinforced random walks and random distributions
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- by R. Daniel Mauldin and S. C. Williams
- Proc. Amer. Math. Soc. 110 (1990), 251-258
- DOI: https://doi.org/10.1090/S0002-9939-1990-1012934-1
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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 $^\# \{ i \leq n:{Z_i} \leq s\} /n$ 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.References
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Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 251-258
- MSC: Primary 60A99; Secondary 60C05, 60G09, 62A15
- DOI: https://doi.org/10.1090/S0002-9939-1990-1012934-1
- MathSciNet review: 1012934