Asymptotic theorems for urn models with nonhomogeneous generating matrices (Q1593611)

A generalized Friedman's urn model consisting of particles of \(K\) distinct types is considered in the case that the generating matrices can differ at each consecutive stage. Asymptotic properties of the urn composition after \(n\) steps are considered as \(n \to \infty \) under some assumptions on eigenvalues and eigenvectors of the generating matrices. Especially, consistency and asymptotic normality of the vector characterizing the composition of the urn are established. Examples of practical applications such as adaptive allocation rules in clinical trials and others are given.