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Zap. Nauchn. Sem. POMI, 2001, Volume 283, Pages 21–36 (Mi znsl1520)  

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.

Full text: PDF file (227 kB)

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Lijoi A., Regazzini E., “Means of a Dirichlet process and multiple hypergeometric functions”, Ann Probab, 32:2 (2004), 1469–1495  crossref  mathscinet  zmath  isi  scopus
    2. James L.F., “Functionals of Dirichlet processes, the Cifarelli-Regazzini identity and Beta-Gamma processes”, Annals of Statistics, 33:2 (2005), 647–660  crossref  mathscinet  zmath  isi  scopus
    3. 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  mathnet  crossref  mathscinet  zmath  elib
    4. 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  crossref  mathscinet  zmath  isi  scopus
    5. 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  crossref  mathscinet  zmath  isi  scopus
    6. 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  crossref  mathscinet  zmath  isi  scopus
    7. Handa K., “The two-parameter Poisson-Dirichlet point process”, Bernoulli, 15:4 (2009), 1082–1116  crossref  mathscinet  zmath  isi  elib  scopus
    8. James L.F., Lijoi A., Prunster I., “On the posterior distribution of classes of random means”, Bernoulli, 16:1 (2010), 155–180  crossref  mathscinet  zmath  isi  elib  scopus
    9. James L.F., “Dirichlet mean identities and laws of a class of subordinators”, Bernoulli, 16:2 (2010), 361–388  crossref  mathscinet  zmath  isi  scopus
    10. 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  mathscinet  isi  elib
    11. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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