Multicolor urn models with reducible replacement matrices

Details Multicolor urn models with reducible replacement matrices Multicolor urn models with reducible replacement matrices

2007-10-08

arxiv.org/abs/0710.1520v3

Bernoulli 2009, Vol. 15, No. 1, 279-295

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/08-BEJ150 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ150

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.

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