Convergence theorems with a stable limit law

Bibliographic Information

Convergence theorems with a stable limit law

by Gerd Christoph and Werner Wolf

(Mathematical research = Mathematische Forschung, 70)

Akademie Verlag, c1992

1st ed

Available at  / 16 libraries

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Note

Bibliography: p. [187]-199

Includes index

Description and Table of Contents

Description

In recent years, more and more mathematical models using stable distributions or sums of random variables approximated by stable laws have been considered in technology, physics, astronomy and economiccs. This work is devoted to topics related to the theory of summation of independent random variables attracted by a stable law. Conditions on pseudomoments and on the tail behaviour of the distribution functions play a crucial role. Berry-Esseen-type inequalities and some problems of probabilities of large deviations are investigated for sums of independent random variables and U-statistics. Asymptotic expansions and non-uniform estimates are developed. Finally, the density problem is treated when the normalized sum of independent or 1-dependent random variables is asymptotically Hoelder continuous. Different examples demonstrate the results.

Table of Contents

  • Properties of pseudomoments and their generalizations
  • Berry-Esseen-type inequalities with a stable limit law
  • asymptotic expansions
  • non-uniform estimates in asymptotic expansions
  • approximations of U-statistics by stable distributions
  • the local limit problem for stable densities.

by "Nielsen BookData"

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Details

  • NCID
    BA20254617
  • ISBN
    • 3055014162
  • Country Code
    gw
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Berlin
  • Pages/Volumes
    199 p.
  • Size
    24 cm
  • Parent Bibliography ID
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