A NEW PROOF OF THE MARKOV–KREIN IDENTITY FOR DISTRIBUTIONS OF MEANS OF DIRICHLET PROCESSES

NATALIA TSILEVICH ANATOLY VERSHIK MARC YOR

Abstract. We present a new simple proof of the Markov–Krein identity for distributions of means of Dirichlet processes. Our approach is based on a close relation of Dirichlet processes to gamma processes and basic properties of the gamma processes.