We give a new integral characterization of the Dirichlet process on a general phase space. To do so, we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. Two applications are a new characterization of the Dirichlet distribution and a marked version of a classical characterization of the Poisson–Dirichlet distribution via invariance and independence properties.

中文翻译：

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Dirichlet 过程的整体表征

我们在一般相空间上给出了狄利克雷过程的新积分表征。为此，我们首先通过大小偏置采样证明了非对称 Beta 分布的特征。两个应用是狄利克雷分布的新表征和泊松-狄利克雷分布通过不变性和独立性的经典表征的标记版本。