Year: 2014
Type: article
Abstract: We propose an approach to analysing the asymptotic behaviour of Pólya urns based on the contraction method. For this, a new combinatorial discrete-time embedding of the evolution of the urn into random rooted trees is developed. A decomposition of these trees leads to a system of recursive distributional equations which capture the distributions of the numbers of balls of each colour. Ideas from the contraction method are used to study such systems of recursive distributional equations asymptotically. We apply our approach to a couple of concrete Pólya urns that lead to limit laws with normal limit distributions, with non-normal limit distributions and with asymptotic periodic distributional behaviour.
Authors: MARGARETE KNAPE, RALPH NEININGER
Institution: Goethe University Frankfurt
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2107927170