TY  - THES
A1  - Knape, Margarete
T1  - Pólya urns via the contraction method
N2  - In this thesis, the asymptotic behaviour of Pólya urn models is analyzed, using an approach based on the contraction method. For this, a combinatorial discrete time embedding of the evolution of the composition of the urn into random rooted trees is used. The recursive structure of the trees is used to study the asymptotic behavior using ideas from the contraction method.
The approach is applied to a couple of concrete Pólya urns that lead to limit laws with normal distributions, with non-normal limit distributions, or with asymptotic periodic distributional behavior.
Finally, an approach more in the spirit of earlier applications of the contraction method is discussed for one of the examples. A general transfer theorem of the contraction method is extended to cover this example, leading to conditions on the coefficients of the recursion that are not only weaker but also in general easier to check.
KW  - Pólya urn
KW  - contraction method
KW  - recursive distributional equation
KW  - weak convergence
KW  - probability metric
Y1  - 2013
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32284
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-322846
PB  - Univ.-Bibliothek
CY  - Frankfurt am Main
ER  -