Advertisement

Infinitely Divisible Laws

  • Yuan Shih Chow
  • Henry Teicher
Chapter
  • 1.7k Downloads
Part of the Springer Texts in Statistics book series (STS)

Abstract

Row sums \( \mathop \sum \nolimits_{i = 1}^{{k_n}} {X_{ni}} \) S of arrays of random variables {Xni1 ≤ ikn >→ ∞n ≥ 1} that are rowwise independent have been considered briefly with respect to the Marcinkiewicz–Zygmund type strong laws of large numbers (Example 10.4.1). In this same context, non-Iterated Logarithm laws and generalizations thereof have been dealt with by H. Cramér and C. Esseen (see references at the end of this chapter). Here, limit distributions of row sums of the variables in such an array will be treated.

Keywords

Stable Distribution Double Sequence Continuity Point Infinitely Divisible Positive Real Function 
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. K. L. ChungA Course in Probability TheoryHarcourt Brace, New York, 1968; 2nd ed., Academic Press, New York, 1974.Google Scholar
  2. H. Cramér, “Su un teorema relativo alla legge uniforme dei grande numeri,”Giornale dell’ Istituto degli Attuari5 (1934), 1–13.Google Scholar
  3. C. Esseen, “Fourier analysis of distribution functions,”Acta Math77 (1945), 79.MathSciNetCrossRefGoogle Scholar
  4. B. V. Gnedenko and A. N. KolmogorovLimit Distributions for Sums of Independent Random VariablesAddison-Wesley, Reading, Mass., 1954.zbMATHGoogle Scholar
  5. P. LévyThéorie de l’addition des variables aléatoiresGarthier-Villars, Paris, 1937; 2nd ed., 1954.zbMATHGoogle Scholar
  6. M. LoéveProbability Theory3rd ed., Van Nostrand, Princeton, 1963; 4th ed., Springer-Verlag, Berlin and New York, 1977–1978.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Yuan Shih Chow
    • 1
  • Henry Teicher
    • 2
  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of StatisticsRutgers UniversityNew BrunswickUSA

Personalised recommendations