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 Andrea Mechtilde Lisbeth Kuntschik (1)
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Rates of convergence for balanced, irreducible Pólya urns with two colours
(2017)

Andrea Mechtilde Lisbeth Kuntschik
 For the class of balanced, irreducible Pólya urn schemes with two colours, say black and white, limit theorems for the number of black balls after n steps are known. Depending on the ratio of the eigenvalues of the replacement matrix, two regimes of limit laws occur: almost sure convergence to a nondegenerate random variable whose distribution depends on the initial composition of the urn and that is known to be not normally distributed and weak convergence to the normal distribution. In this thesis, upper bounds on the rates of convergence in both the nonnormal limit case and the normal limit case are given.