Multicolor urn models with reducible replacement matrices
Bose, Arup ; Dasgupta, Amites ; Maulik, Krishanu
Bernoulli, Tome 15 (2009) no. 1, p. 279-295 / Harvested from Project Euclid
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.
Publié le : 2009-02-15
Classification:  martingale,  reducible stochastic replacement matrix,  urn model,  variance mixture of normal
@article{1233669892,
     author = {Bose, Arup and Dasgupta, Amites and Maulik, Krishanu},
     title = {Multicolor urn models with reducible replacement matrices},
     journal = {Bernoulli},
     volume = {15},
     number = {1},
     year = {2009},
     pages = { 279-295},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1233669892}
}
Bose, Arup; Dasgupta, Amites; Maulik, Krishanu. Multicolor urn models with reducible replacement matrices. Bernoulli, Tome 15 (2009) no. 1, pp.  279-295. http://gdmltest.u-ga.fr/item/1233669892/