Advertisement

Limit theorems in the problems of stability

  • R. Yanushkevichius
  • O. Yanushkevichiene
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 982)

Keywords

Limit Theorem Central Limit Theorem Identical Distribution Main Lemma Auxiliary Lemma 
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.
    Polya G. Herleitung des Gausschen fehlergesetzes aus einer functionalgleichung.-Math.Z.1923, B.18, s. 96–108.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Prohorov Yu.V., Fiš M. A characteristic property of normal distribution in Hilbert space.-Teorija verojatn i ee primen., 1957, v.2, No. 4, p. 475–477 (in Russian).Google Scholar
  3. 3.
    Kagan A.M., Linnik Yu.V., Rao S.R. Characterization problems of mathematical statistics. New York: J.Wiley, 1973.zbMATHGoogle Scholar
  4. 4.
    Zinger A.A., Yanushkevichius R.V. On a theorem of characterization by the coincidence of statistics distribution and it’s stability.-In: Problemy ustoičivosti stohastičeskih modelei: Institute for Systems Studies, 1980, p. 32–46 (in Russian).Google Scholar
  5. 5.
    Zinger A.A. Yanushkevichius R.V. Stability of one characterization theorem of Ju.V.Linnik.-In: Problemy ustoičivosti stohastičeskih modelei. Moscow: Institute for Systems Studies, 1981, p. 24–30 (in Russian).Google Scholar
  6. 6.
    Šiganov I.S. Metrical approach to the studies of the Polya’s theorem on a characterization of normal distribution.-In: Problemy ustoičivosti stohastičeskih modelei. Moscow: Institute for Systems Studies, 1981, p. 145–154 (in Russian).Google Scholar
  7. 7.
    Yanushkevichius R.V. Estimates of stability of normal distribution characterization in the G.Polya’s theorem.-Zapiski Nayčn. Seminarov LOMI, 1979, v, 87, p. 196–205 (in Russian).MathSciNetGoogle Scholar
  8. 8.
    Loève M. Probability theory. D. van Nostrand comp.: Princeton, 1960.zbMATHGoogle Scholar
  9. 9.
    Yanushkevichius R.V. Estimate of stability of the normal law characterization by the distribution coincidence of the monome and the statistic.-Lit. Mathem. Sb., 1980, v. 20, No. 2, p. 195–206 (in Russian).MathSciNetGoogle Scholar
  10. 10.
    Meshalkin L.D. On the robustness of some characterizations of the normal distribution.-Ann. Math. Statist., 1968, v. 39, No. 5, p. 1747–1750.MathSciNetzbMATHGoogle Scholar
  11. 11.
    Petrov V.V. Sums of independent random variables. Moscow: Nauka, 1972, (in Russian).zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • R. Yanushkevichius
    • 1
  • O. Yanushkevichiene
    • 1
  1. 1.VilniusRussia

Personalised recommendations