Resumen de Asymptotics for the number of replacements in a generalized Pólya urn model

Fernando Plo , Henar Urmeneta Martín-Calero , Miguel San Miguel Marco , José Antonio Moler Cuiral

• There are three processes associated to a generalized Pólya urn model. First, the process that represents the proportion of balls of each type in the urn. As in each step a ball is drawn from the urn, its type is noted, and it is placed back in the urn, the second process represents the proportion of balls of each type that have been drawn from the urn. As the replacement policy consists in applying in each step one out of K different actions, the third process represents the proportion of times that each action (replacement) has been applied. This third process has not attracted as much attention as the others in the probabilistic literature. In this work we present conditions under which almost sure convergence results and central limit theorems are obtained for it. We illustrate these results with an application to adaptive clinical trials and random data structures