Bernoulli

  • Bernoulli
  • Volume 15, Number 1 (2009), 279-295.

Multicolor urn models with reducible replacement matrices

Arup Bose, Amites Dasgupta, and Krishanu Maulik

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Abstract

Consider the multicolored urn model where, after every draw, balls of the different colors are added to the urn in a proportion determined by a given stochastic replacement matrix. We consider some special replacement matrices which are not irreducible. For three- and four-color urns, we derive the asymptotic behavior of linear combinations of the number of balls. In particular, we show that certain linear combinations of the balls of different colors have limiting distributions which are variance mixtures of normal distributions. We also obtain almost sure limits in certain cases in contrast to the corresponding irreducible cases, where only weak limits are known.

Article information

Source
Bernoulli, Volume 15, Number 1 (2009), 279-295.

Dates
First available in Project Euclid: 3 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.bj/1233669892

Digital Object Identifier
doi:10.3150/08-BEJ150

Mathematical Reviews number (MathSciNet)
MR2546808

Zentralblatt MATH identifier
1206.60008

Keywords
martingale reducible stochastic replacement matrix urn model variance mixture of normal

Citation

Bose, Arup; Dasgupta, Amites; Maulik, Krishanu. Multicolor urn models with reducible replacement matrices. Bernoulli 15 (2009), no. 1, 279--295. doi:10.3150/08-BEJ150. https://projecteuclid.org/euclid.bj/1233669892


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