Pólya urns via the contraction method
- 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.
Download full text files
Additional Services
| Author: | Margarete Knape |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-322846 |
| Publisher: | Univ.-Bibliothek |
| Place of publication: | Frankfurt am Main |
| Referee: | Ralph NeiningerORCiDGND, Hosam M. Mahmoud |
| Advisor: | Ralph Neininger |
| Document Type: | Doctoral Thesis |
| Language: | English |
| Date of Publication (online): | 2013/11/10 |
| Year of first Publication: | 2013 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Granting Institution: | Johann Wolfgang Goethe-Universität |
| Date of final exam: | 2013/11/08 |
| Release Date: | 2013/11/19 |
| Tag: | Pólya urn; contraction method; probability metric; recursive distributional equation; weak convergence |
| Page Number: | 84 |
| HeBIS-PPN: | 33384145X |
| Institutes: | Informatik und Mathematik / Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Deutsches Urheberrecht |
