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Zap. Nauchn. Sem. POMI, 2001, Volume 283, Pages 21–36
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This article is cited in 10 scientific papers (total in 11 papers)
Remarks on the Markov–Krein identity and quasi-invariance of the gamma process
A. M. Vershika, M. Yorb, N. V. Tsilevicha
a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Université Pierre & Marie Curie, Paris VI
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.
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English version:
Journal of Mathematical Sciences (New York), 2004, 121:3, 2303–2310
Bibliographic databases:
 
UDC:
512
Received: 15.11.2001
Citation:
A. M. Vershik, M. Yor, N. V. Tsilevich, “Remarks on the Markov–Krein identity and quasi-invariance of the gamma process”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VI, Zap. Nauchn. Sem. POMI, 283, POMI, St. Petersburg, 2001, 21–36; J. Math. Sci. (N. Y.), 121:3 (2004), 2303–2310
Citation in format AMSBIB
\Bibitem{VerYorTsi01}
\by A.~M.~Vershik, M.~Yor, N.~V.~Tsilevich
\paper Remarks on the Markov--Krein identity and quasi-invariance of the gamma process
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~VI
\serial Zap. Nauchn. Sem. POMI
\yr 2001
\vol 283
\pages 21--36
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1520}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1879060}
\zmath{https://zbmath.org/?q=an:1069.60046}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2004
\vol 121
\issue 3
\pages 2303--2310
\crossref{https://doi.org/10.1023/B:JOTH.0000024611.30457.a8}
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Lijoi A., Regazzini E., “Means of a Dirichlet process and multiple hypergeometric functions”, Ann Probab, 32:2 (2004), 1469–1495
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A. M. Vershik, “On F. A. Berezin and his work on representations of current groups”, J. Math. Sci. (N. Y.), 141:4 (2007), 1385–1389
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Donati-Martin C., Yor M., “Some explicit Krein representations of certain subordinators, including the Gamma process”, Publications of the Research Institute For Mathematical Sciences, 42:4 (2006), 879–895
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James L.F., Lijoi A., Prunster I., “Distributions of linear functionals of two parameter Poisson-Dirichlet random measures”, Annals of Applied Probability, 18:2 (2008), 521–551
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von Renesse M.-K., Yor M., Zambotti L., “Quasi-invariance properties of a class of subordinators”, Stochastic Processes and Their Applications, 118:11 (2008), 2038–2057
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Handa K., “The two-parameter Poisson-Dirichlet point process”, Bernoulli, 15:4 (2009), 1082–1116
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James L.F., Lijoi A., Prunster I., “On the posterior distribution of classes of random means”, Bernoulli, 16:1 (2010), 155–180
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James L.F., “Dirichlet mean identities and laws of a class of subordinators”, Bernoulli, 16:2 (2010), 361–388
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Kachanovsky N.A., “Elements of a Non-Gaussian Analysis on the Spaces of Functions of Infinitely Many Variables”, Ukrainian Math J, 62:9 (2011), 1420–1448
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V. M. Buchstaber, M. I. Gordin, I. A. Ibragimov, V. A. Kaimanovich, A. A. Kirillov, A. A. Lodkin, S. P. Novikov, A. Yu. Okounkov, G. I. Olshanski, F. V. Petrov, Ya. G. Sinai, L. D. Faddeev, S. V. Fomin, N. V. Tsilevich, Yu. V. Yakubovich, “Anatolii Moiseevich Vershik (on his 80th birthday)”, Russian Math. Surveys, 69:1 (2014), 165–179
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