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Journal Article
LIMIT THEOREMS FOR RANDOM TRIANGULAR URN SCHEMES
RAFIK AGUECH
Journal of Applied Probability
Vol. 46, No. 3 (SEPTEMBER 2009), pp. 827-843
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/25662463
Page Count: 17
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Topics: Random variables, Martingales, Mathematical theorems, Law of large numbers, Central limit theorem, Matrices, Integers, Perceptron convergence procedure
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Abstract
In this paper we study a generalized Pólya urn with balls of two colors and a random triangular replacement matrix. We extend some results of Janson (2004), (2005) to the case where the largest eigenvalue of the mean of the replacement matrix is not in the dominant class. Using some useful martingales and the embedding method introduced in Athreya and Karlin (1968), we describe the asymptotic composition of the urn after the nth draw, for large n.
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Journal of Applied Probability © 2009 Applied Probability Trust