Abstract
We present a simple proof of the Markov–Krein identity for distributions of means of linear functionals of the Dirichlet process and its various generalizations. The key idea is to use the representation of the Dirichlet process as the normalized gamma process and fundamental properties of gamma processes. Bibliography: 19 titles.
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Vershik, A.M., Yor, M. & Tsilevich, N. On the Markov–Krein Identity and Quasi-Invariance of the Gamma Process. Journal of Mathematical Sciences 121, 2303–2310 (2004). https://doi.org/10.1023/B:JOTH.0000024611.30457.a8
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DOI: https://doi.org/10.1023/B:JOTH.0000024611.30457.a8