Lithuanian Mathematical Journal

, Volume 38, Issue 4, pp 318–327 | Cite as

Functional limit theorems for sums of independent random variables with random coefficients

  • N. Chuprunov
Article

Keywords

Random Process Independent Random Variable Random Coefficient Independent Increment Probability Metrics 

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References

  1. 1.
    V. M. Zolotarev,The Univariate Stable Distributions [in Russian], Nauka, Moscow (1983).Google Scholar
  2. 2.
    B. V. Gnedenko and A. N. Kolmogorov,Limit Distributions for the Sums of Independent Random Variables, Addison-Wesley, Reading (1954).Google Scholar
  3. 3.
    E. Gine, M. B. Marcus, and J. Zinn, On random multipliers in the theorem withp-stable limit, 0<p<2, in:Probability in Banach Spaces, Proc. of VI Int. Conf., Birkhäuser, Boston (1990), pp. 120–149.Google Scholar
  4. 4.
    E. Gine and J. Zinn,L pmultipliers in the central limit theorem withp-stable limit, in:Probability Theory on Vector Spaces, IV, Lecture Notes in Math., 139, Springer-Verlag (1987), pp. 74–81.Google Scholar
  5. 5.
    A. N. Chuprunov, On convergence in law of sums of independent random elements with random coefficients,Stability Problems for Stochastic Models, VSR, 41–54 (1993).Google Scholar
  6. 6.
    Yu. V. Prokhorov, Convergence of random processes and limit theorems of probability theory.Theory Probab. Appl.,1 (2), 117–238 (1956).CrossRefGoogle Scholar
  7. 7.
    V. M. Kruglov, The weak convergence of random polygonal lines to the Wiener process,Theory Probab. Appl.,30 (2), 209–218 (1985).MATHMathSciNetGoogle Scholar
  8. 8.
    V. M. Zolotarev, Center and spread of a probability distribution,Sov. Math. Dokl.,11, 1329–1331 (1970).MATHGoogle Scholar
  9. 9.
    V. M. Zolotarev,Modern Theory of Summation of Random Variables, VSP, Utrecht (1997).MATHGoogle Scholar
  10. 10.
    I. I. Gikhman and A. V. Skorokhod,Introduction to the Theory of Random Processes [in Russian], Nauka, Moscow (1977).MATHGoogle Scholar
  11. 11.
    J. Mačys, Sur la convergence des réparitions de sommes de variables aléatoires indépendantes vers les lois de la classeI 0 de Linnik,C. R. Acad. Sci. Paris,267, 316–317 (1968).Google Scholar
  12. 12.
    J. Mačys, Limit theorems in non-classical settings,Theory Probab. Appl.,16(1), 172–180 (1971).Google Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • N. Chuprunov

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