We consider weak and strong Gaussian approximations for a two-color generalized Friedman's urn model with homogeneous and nonhomogeneous generating matrices. In particular, the functional central limit theorems and the laws of iterated logarithm are obtained. As an application, we obtain the asymptotic properties for the randomized-play-the-winner rule. Based on the Gaussian approximations, we also get some variance estimators for the urn model.
Publié le : 2002-11-14
Classification:
Gaussian approximation,
the law of iterated logarithm,
functional central limit theorems,
urn model,
nonhomogeneous generating matrix,
randomized play-the-winner rule,
62G10,
60F15,
62E10
@article{1037125857,
author = {Bai, Z. D. and Hu, Feifang and Zhang, Li-Xin},
title = {Gaussian approximation theorems for urn models and their applications},
journal = {Ann. Appl. Probab.},
volume = {12},
number = {1},
year = {2002},
pages = { 1149-1173},
language = {en},
url = {http://dml.mathdoc.fr/item/1037125857}
}
Bai, Z. D.; Hu, Feifang; Zhang, Li-Xin. Gaussian approximation theorems for urn models and their applications. Ann. Appl. Probab., Tome 12 (2002) no. 1, pp. 1149-1173. http://gdmltest.u-ga.fr/item/1037125857/