Regimes de liderança em urnas de Pólya não-lineares

Abstract

Pólya's urn model is a stochastic process in which colored balls in an urn represent the objects of interest. A ball is drawn randomly and then is placed back in the urn with another additional ball of the same color. This process is repeated n times. We say that a color leads in the urn when this color has more balls. The original model is linear, but can be generalized to incorporate nonlinear effects. The goal of this dissertation is to study the evolution of the nonlinear urn's population in terms of leadership. In the linear case, the number of balls of each color grows linearly with time and for a large enough n, one of the colors takes the lead. In the nonlinear case, we conclude that there are three possibilities: from a random moment, either only one of the colors will be drawn or both colors will continue to be drawn, but there will be a leading color; or there will be infinite leadership changes. We use Rubin's construction as the main tool.