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Strong convergence of proportions in a multicolor Pólya urn

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  14 July 2016

Raúl Gouet
Raúl Gouet*
Affiliation:
Universidad de Chile
*
∗Postal address: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170/3, Santiago, Chile.
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Abstract

We prove strong convergence of the proportions Un/Tn of balls in a multitype generalized Pólya urn model, using martingale arguments. The limit is characterized as a convex combination of left dominant eigenvectors of the replacement matrix R, with random Dirichlet coefficients.

Keywords

URN MODELLIMIT THEOREMSMARTINGALES

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60K99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 426 - 435
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

Partial funding provided by FONDECYT under grants 0911/92 and 1950534.

References

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