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An Integral Characterization of the Dirichlet Process

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Abstract

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.

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Acknowledgements

I wish to thank Lorenzo Dello Schiavo for drawing my attention to the topic of the paper and the referee for making several helpful comments.

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  1. Institute of Stochastics, Karlsruhe Institute of Technology, 76131, Karlsruhe, Germany

    Günter Last

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  1. Günter Last
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Correspondence to Günter Last.

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Last, G. An Integral Characterization of the Dirichlet Process. J Theor Probab 33, 918–930 (2020). https://doi.org/10.1007/s10959-019-00923-y

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  • DOI: https://doi.org/10.1007/s10959-019-00923-y

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