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Limit Theorems for Random Triangular URN Schemes
Published online by Cambridge University Press: 14 July 2016
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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- Research Article
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- Copyright © Applied Probability Trust 2009
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