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On the Markov-Krein identity and quasi-invariance of the gamma process. (English. Russian original) Zbl 1069.60046

J. Math. Sci., New York 121, No. 3, 2303-2310 (2004); translation from Zap. Nauchn. Semin. POMI 283, 21-36 (2001).
Summary: 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.

MSC:

60G51 Processes with independent increments; Lévy processes
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