Nonlinear and unbalanced urn models with two types of strategies: a stochastic approximation point of view

Abstract

AbstractIn this paper, we treat a nonlinear and unbalanced $2$-color urn scheme, subjected to two different nonlinear drawing rules, depending on the color withdrawn. We prove a central limit theorem as well as a law of large numbers for the urn composition. We also give an estimate of the mean and variance of both types of balls.