Strong laws for balanced triangular urns
Arup Bose, Amites Dasgupta, and Krishanu Maulik
Source: J. Appl. Probab.
Volume 46, Number 2
(2009), 571-584.
Abstract
Consider an urn model whose replacement matrix is triangular, has
all nonnegative entries, and the row sums are all equal to 1. We
obtain strong laws for the counts of balls corresponding to each
color. The scalings for these laws depend on the diagonal elements
of a rearranged replacement matrix. We use these strong laws to
study further behavior of certain three-color urn models.
Primary Subjects: 60G70, 60F05
Secondary Subjects: 60F10
Keywords: Urn model; balanced triangular replacement matrix
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1245676107
Digital Object Identifier: doi:10.1239/jap/1245676107
Zentralblatt MATH identifier:
05578826
Mathematical Reviews number (MathSciNet):
MR2535833
References
Bai Z. D. and Hu, F. (1999). Asymptotic theorems for urn models with nonhomogeneous generating matrices. Stoch. Process. Appl. 80, 87--101.
Bose, A., Dasgupta, A. and Maulik, K. (2009). Multicolor urn models with reducible replacement matrices. Bernoulli 15, 279--295.
Flajolet, P., Dumas, P. and Puyhaubert, V. (2006). Some exactly solvable models of urn process theory. Discrete Math. Theoret. Computer Sci. AG, 59--118.
Gouet, R. (1997). Strong convergence of proportions in a multicolor Pólya urn. J. Appl. Prob. 34, 426--435.
Janson, S. (2006). Limit theorems for triangular urn schemes. Prob. Theory Relat. Fields 134, 417--452.
