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An application of Fourier methods to the problem of sharpening the Berry-Esseen inequality

  • Paul van Beek
Article

Keywords

Fourier Stochastic Process Probability Theory Mathematical Biology Fourier Method 
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References

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    van Beek, P.: Fourier-analytische Methoden zur VerschÄrfung der Berry-Esseen Schranke. Doctoral dissertation Bonn 1971.Google Scholar
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    Berry, A.C.: The accuracy of the Gaussian approximation to the sum of independent variates. Trans. Amer. Math. Soc. 49, 122–136 (1941).Google Scholar
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    Esseen, C.G.: On the Liapunov limit of error in the theory of probability. Ark. Mat. Astr. Fys. 28A, 1–19 (1942).Google Scholar
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    Esseen, C.G.: A moment inequality with an application to the central limit theorem. Skand. Aktuarietidskr. 39, 160–170 (1956).Google Scholar
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    Goldberg, R.R.: Fourier Transforms. Cambridge Tracts in mathematics and mathematical Physics 52, Cambridge: University Press 1970.Google Scholar
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    Zolotarev, V.M.: On the closeness of the distributions of two sums of independent random variables. Theor. Probab. Appl. 10, 472–479 (1965).Google Scholar
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    Zolotarev, V.M.: An absolute estimate of the remainder term in the central limit theorem. Theor. Probab. Appl. 11, 95–105 (1966).Google Scholar
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    Zolotarev, V.M.: Some inequalities in probability theory and their application in sharpening the Lyapunov theorem. Soviet Math. Dok. 8, 1427–1430 (1967).Google Scholar
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    Zolotarev, V.M.: A sharpening of the inequality of Berry-Esseen. Z. Wahrscheinlichkeitstheorie verw. Gebiete 8, 332–342 (1967).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Paul van Beek
    • 1
  1. 1.Philips ISAREindhovenThe Netherlands

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