Stochastic Recurrences and their Applications to the Analysis of Partition-Valued Processes

Abstract

The thesis consists of two parts. In the first part (Chapter 1) a new technique is developed for the asymptotic analysis of the moments of linear random recurrences, and some general results are presented for the absorption times of non-increasing Markov chains. In the second part (Chapters 2 and 3) we establish new results for two models where linear distributional recurrences occur: these are the stick-breaking partitions (Chapter 2) and exchangeable coalescents (Chapter 3).