Convergence theorems with a stable limit law

著者

• Christoph, Gerd
• Wolf, Werner

書誌事項

Convergence theorems with a stable limit law

by Gerd Christoph and Werner Wolf

（Mathematical research = Mathematische Forschung, 70）

Akademie Verlag, c1992

1st ed

注記

Bibliography: p. [187]-199

Includes index

内容説明・目次

内容説明

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.

目次

• 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.

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詳細情報

• NII書誌ID(NCID): BA20254617
• ISBN:
  • 3055014162
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Berlin
• ページ数/冊数: 199 p.
• 大きさ: 24 cm
• 親書誌ID:
  • BA00289776