Advertisement

Journal of Mathematical Sciences

, Volume 189, Issue 6, pp 950–953 | Cite as

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

  • S. A. Maslenkov
Article
  • 33 Downloads

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.

Keywords

Joint Distribution Gaussian Process Conditional Distribution Null Vector Distinguishable Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. F. Kolchin, B. A. Sevastianov, and V. P. Chistyakov, Random accommodations, Nauka, Moscow (1976).Google Scholar
  2. 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.Google Scholar
  3. 3.
    D. A. Darling, “Some limits theorems associated with multinomial trials,” in: Proc. 5th Berkeley Symp. Math. Stat. Probab., 345–350.Google Scholar
  4. 4.
    S. Karlin, Central limit theorems for certain infinite urn schemes.,” J. Math. Mech., 17, No.4, 373–401 (1967).MathSciNetMATHGoogle Scholar
  5. 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. 6.
    A. N. Shiryaev, Probability, Nauka, Moscow (1980).MATHGoogle Scholar
  7. 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. 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. 9.
    I. I. Gikhman and A. V. Skorokhod, The Theory of Stochastic Processes, Nauka, Moscow (1965).Google Scholar
  10. 10.
    P. Billingsli, Convergence of Probabilistic Measures, Nauka, Moscow (1977).Google Scholar
  11. 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.Google Scholar
  12. 12.
    E. M. Kudlaev, “Weak convergence of distributions of separable statistics,” Teor. Veroyatn. Primen., 42, No.1, 85–107 (1997).MathSciNetMATHGoogle Scholar
  13. 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).Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsLomonosov Moscow State UniversityMoscowRussia

Personalised recommendations