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Decomposable Statistics and Random Placement of Particles over a Countable Set of Cells*

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In the paper, the scheme of independent particle allocation is considered. A connection is demonstrated between finite-dimensional distributions for the process of the number of particles assigned to the k-th cell and the conditional distribution of independent Poisson distributed random variables. Conditions are specified for the convergence of these distributions to finite-dimensional distributions of the Gaussian process. A certain scheme of dependent particle allocation on a countable set of cells is introduced and investigated.

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References

  1. V. F. Kolchin, B. A. Sevastianov, and V. P. Chistyakov, Random accommodations, Nauka, Moscow (1976).

    Google Scholar 

  2. V. A. Ivanov, G. I. Ivchenko, and Y. I. Medvedev, “Discrete problems in probability theory,” in: Itogi Nauki i Tekhniki. Seriya “Teoriya Veroyatnostei. Matematicheskaya Statistika. Teoreticheskaya Kibernetika”, Vol.22, Russian Institute for Scientific and Technical Information, Russian Academy of Sciences, Moscow (1984), 3–60.

  3. D. A. Darling, “Some limits theorems associated with multinomial trials,” in: Proc. 5th Berkeley Symp. Math. Stat. Probab., 345–350.

  4. S. Karlin, Central limit theorems for certain infinite urn schemes.,” J. Math. Mech., 17, No.4, 373–401 (1967).

    MathSciNet  MATH  Google Scholar 

  5. B. V. Gnedenko and E. M. Kudlaev, “On random variables caused by sums of independent random variables,” Vestn. MGU, Ser. Mat. Mekh., No.1, 23–31 (1995).

    Google Scholar 

  6. A. N. Shiryaev, Probability, Nauka, Moscow (1980).

    MATH  Google Scholar 

  7. E. M. Kudlaev and S. A. Maslenkov, “On marginal distributions of the process of placing the particles in a countable number of cells,” Surveys in Applied and Industrial Mathematics [in Russian], 8, No.1, 248 (2001).

    Google Scholar 

  8. E. M. Kudlaev and S. A. Maslenkov, “On the convergence of finite-dimensional distributions of the process of independent distribution of particles in a countable set of cells,” Surveys in Applied and Industrial Mathematics [in Russian], 8, No.2, 782 (2001).

    Google Scholar 

  9. I. I. Gikhman and A. V. Skorokhod, The Theory of Stochastic Processes, Nauka, Moscow (1965).

    Google Scholar 

  10. P. Billingsli, Convergence of Probabilistic Measures, Nauka, Moscow (1977).

    Google Scholar 

  11. A. N. Trunov, “Limit theorems in the problem of distributing identical particles in different cells,” in: Proc. Steklov Inst. Math., Vol.177, Nauka, Moscow (1986), 147–164.

  12. E. M. Kudlaev, “Weak convergence of distributions of separable statistics,” Teor. Veroyatn. Primen., 42, No.1, 85–107 (1997).

    MathSciNet  MATH  Google Scholar 

  13. R. R. Bahadur, “On the number of distinct values in a large sample from an infinite discrete distribution,” Proc. of the National Institute of Sciences of India, 26 A, Supp.II, 67–75 (1960).

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    S. A. Maslenkov

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  1. S. A. Maslenkov
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Correspondence to S. A. Maslenkov.

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*Research supported by the Russian Foundation for Basic Research, project No. 01–01–00644.

Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 16, pp. 160–167, 2002.

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Maslenkov, S.A. Decomposable Statistics and Random Placement of Particles over a Countable Set of Cells*. J Math Sci 189, 950–953 (2013). https://doi.org/10.1007/s10958-013-1236-6

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  • DOI: https://doi.org/10.1007/s10958-013-1236-6

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