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Strong Laws for Balanced Triangular Urns

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Arup Bose ,
Amites Dasgupta  and
Krishanu Maulik
Arup Bose*
Affiliation:
Indian Statistical Institute
Amites Dasgupta*
Affiliation:
Indian Statistical Institute
Krishanu Maulik*
Affiliation:
Indian Statistical Institute
*
∗Postal address: Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
∗Postal address: Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
∗Postal address: Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
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Abstract

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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.

Keywords

Urn modelbalanced triangular replacement matrix

MSC classification

Secondary: 60G70: Extreme value theory; extremal processes 60F05: Central limit and other weak theorems 60F10: Large deviations
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 571 - 584
Copyright
Copyright © Applied Probability Trust 2009 

References

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