Advertisement

Lithuanian Mathematical Journal

, Volume 36, Issue 4, pp 388–399 | Cite as

A rate of convergence in the poissonian representation of stable distributions

  • M. Ledoux
  • V. Paulauskas
Article

Keywords

Stable Distribution Standard Gaussian Random Variable Stable Random Variable Symmetric Random Variable Symmetric Stable Distribution 
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.
    A. C. Berry, The accuracy of the Gaussian approximation to the sum of independent variates,Trans. Amer. Math. Soc.,49, 122–136 (1941).CrossRefMathSciNetMATHGoogle Scholar
  2. 2.
    G. Christoph and W. Wolf,Convergence Theorems with a Stable Limit Law, Mahematical Research, 70, Academie-Verlag (1992).Google Scholar
  3. 3.
    C. G. Esseen, Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law,Acta Math.,77, 1–125 (1945).CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    I. A. Ibragimov and Yu. V. Linnik,Independent and Stationary Sequences of Random Variables, Walters-Noorhoff, Groningen (1971).MATHGoogle Scholar
  5. 5.
    A. Janicki and P. Kokoszka, Computer investigation of the rate of convergence of LePage type series to α-stable random variables,Statistics,23, 365–373 (1992).CrossRefMathSciNetMATHGoogle Scholar
  6. 6.
    A. Janicki and P. Kokoszka, On the rate of convergence of LePage type series to finite dimensional distributions of Levy motion, 1992 (Preprint).Google Scholar
  7. 7.
    A. Janicki and A. Weron,Simulation and Chaotic Behavior of α-Stable Stochastic Processes, Marcel Dekker, New York (1994).Google Scholar
  8. 8.
    M. Ledoux and M. Talagrand,Probability in Banach Spaces, Springer-Verlag, Berlin (1991).MATHGoogle Scholar
  9. 9.
    R. LePage,Multidimensional infinitely divisible variables and processes. Part I, Technical Report No 292, Statistics Department, Stanford, 1980. Reprinted inLecture Notes in Math.,1391 (1989).Google Scholar
  10. 10.
    R. LePage, Multidimensional infinitely divisible variables and processes. Part II,Lecture Notes in Math.,860, 279–284 (1981).CrossRefMathSciNetGoogle Scholar
  11. 11.
    R. LePage, M. Woodroofe, and J. Zinn, Convergence to stable distribution via order statistics,Ann. Probab.,9, 624–632 (1981).CrossRefMathSciNetMATHGoogle Scholar
  12. 12.
    E. Lukacs,Developments in Characteristic Function Theory, Vol. 4, MacMillan Pub. Co. Inc. (1983).Google Scholar
  13. 13.
    M. B. Marcus and G. Pisier,Random Fourier Series with Applications to Harmonic Analysis, Ann. Math. Stud.,101, Princeton Univ. Press (1981).Google Scholar
  14. 14.
    V. Paulauskas, Estimate of remainder in limit theorem in the case of stable limit law,Lith. Math. J.,14, 165–187 (1974).MathSciNetGoogle Scholar
  15. 15.
    V. V. Petrov,Sums of Independent Random Variables, Springer-Verlag, Berlin (1975).Google Scholar
  16. 16.
    G. Samorodnitsky and M. S. Taqqu,Stable non-Gaussian Random Processes. Stochastic Models with Infinite Variance, Chapman and Hall, New York-London (1994).MATHGoogle Scholar
  17. 17.
    V. M. Zolotarev,Contemporary Theory of Summation of Independent Random Variables [in Russian], Nauka, Moscow (1986).Google Scholar
  18. 18.
    V. M. Zolotarev,One Dimensional Stable Distributions, Transl, of Math. Monographs, Amer. Math. Soc., Providence, Rhode Island (1986).MATHGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • M. Ledoux
    • 1
    • 2
    • 3
  • V. Paulauskas
    • 1
    • 2
    • 3
  1. 1.Département de MathématiquesUniversité Paul-SabatierToulouseFrance
  2. 2.Vilnius UniversityVilniusLithuania
  3. 3.Institute of Mathematics and InformaticsVilniusLithuania

Personalised recommendations