Convergence theorems with a stable limit law
Author(s)
Bibliographic Information
Convergence theorems with a stable limit law
（Mathematical research = Mathematische Forschung, 70）
Akademie Verlag, c1992
1st ed
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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"
