Poisson-Dirichlet分布及可逆测度值过程

Reversible measure-valued processes associated with the Poisson-Dirichlet distribution

Poisson-Dirichlet分布是定义在无穷维单纯形上的概率.它刻画了一个取值为离散概率的随机变量的分布.与Poisson-Dirichlet分布密切相关的随机测度包括GEM (Griffiths-Engen-McCloskey)分布、Dirichlet过程、两参数Dirichlet过程和两参数Poisson-Dirichlet分布等.构造与这些分布相应的测度值过程是近些年比较活跃的研究课题.本文介绍近年来这方面的发展状况,并给出一些待研究的问题.

The Poisson-Dirichlet distribution is a probability on the space of in?nite dimensional simplex.It is the distribution of a discrete-probability-valued random variable.The closely associated random measures include the GEM distribution,the Dirichlet process and their two-parameter generalizations.One of the active areas for research in modern probability is concerned with the construction of reversible measure-valued processes associated with these random measures.This article will survey recent development in this area and list a few interesting problems for further consideration.