Analysis of Diminishing urn Models

Abstract

I will present a class of 2x2 Polya-Eggenberger urn models with diminishing character. Consideration of this class of urn models was mainly motivated by several concrete problems, including the pills problem, the so-called cannibal urns, and sampling without replacement. 　　　Many new distributional results will be given. The tools we use are based on generating functions, partial differential equations and the method of moments. Generalizations to higher dimensions will also be briefly discussed.