Asymptotic behavior of Dirichlet process and related random measures

Dirichlet process is an atomic-valued random measure. It was introduced by Ferguson (1973) with motivation from Bayesian statistics.Pitman and Yor generalized the process to the two-parameter setting in 1990s.It has since found applications in a wide range of subjects including Bayesian statistics, biology, communication, economy, finance, genetics,and machine learning. Driven by various applications, there has been active study of asymptotic behavior of this class of processes.This paper provides a brief survey on recent work by the author and collaborators.