Ferguson-Dirichlet過程在N維空間上的隨機函數分配

Abstract

自從Ferguson (1973) 首先提出Ferguson-Dirichlet過程後，就一直有很多學者研究它的隨機函數。本研究中，我們將首先研究及給予Ferguson-Dirichlet過程在n-維球體上的隨機函數之機率密度函數，這些將是低維度結果的相當重要的擴充，同時，我們也將研究以及提供Ferguson-Dirichlet過程在有界n-維空間上隨機過程的機率密度函數。

Since Ferguson-Dirichlet process was first introduced by Ferguson (1973), many researchers have studied its random functional. In this research, we first study and give the probability density functions of the random functional of the Ferguson-Dirichlet process over any n-dimensional sphere. These would be a very important generalization of the current low dimensional results. In addition, we shall also study and provide the probability density functions of the random functional of the Ferguson-Dirichlet process over any n-dimensional bounded space.