Central limit theorems for multicolour urn models

  • Urn models are simple examples for random growth processes that involve various competing types. In the study of these schemes, one is generally interested in the impact of the specific form of interaction on the allocation of elements to the types. Depending on their reciprocal action, effects of cancellation and self-reinforcement become apparent in the long run of the system. For some urn models, the influencing is of a smoothing nature and the asymptotic allocation to the types is close to being a result of independent and identically distributed growth events. On the contrary, for others, almost sure random tendencies or logarithmically periodic terms emerge in the second growth order. The present thesis is devoted to the derivation of central limit theorems in the latter case. For urns of this kind, we use a "non-classical" normalisation to derive asymptotic joint normality of the types. This normalisation takes random tendencies and phases into account and consequently involves random centering and, also, possibly random scaling.

Download full text files

Export metadata

Author:Noela MüllerORCiDGND
Place of publication:Frankfurt am Main
Referee:Ralph NeiningerORCiDGND, Rudolf GrübelORCiDGND
Document Type:Doctoral Thesis
Date of Publication (online):2018/02/01
Year of first Publication:2017
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Granting Institution:Johann Wolfgang Goethe-Universität
Date of final exam:2017/09/22
Release Date:2018/01/11
Page Number:110
Institutes:Informatik und Mathematik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):License LogoDeutsches Urheberrecht