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Gaussian approximation theorems for urn models and their applications. (English) Zbl 1014.60025
The authors consider weak and strong Gaussian approximations for a two-color generalized Friedman’s urn model with homogeneous and nonhomogeneous generating matrices. The authors present functional central limit theorems and the laws of iterated logarithm. As an application, asymptotic properties for the randomized play-the-winner rule are obtained. Based on the Gaussian approximations, the authors also get some variance estimators for the urn model.

MSC:
60F15 Strong limit theorems
60F05 Central limit and other weak theorems
62E10 Characterization and structure theory of statistical distributions
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[22] CHARLOTTESVILLE, VIRGINIA 22904-4135 E-MAIL: fh6e@virginia.edu L.-X. ZHANG DEPARTMENT OF MATHEMATICS ZHEJIANG UNIVERSITY, XIXI CAMPUS ZHEJIANG, HANGZHOU 310028 P.R. CHINA E-MAIL: lxzhang@mail.hz.zj.cn
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