Estimates for the rapid decay of concentration functions of n-fold convolutions

Götze F, Zaitsev AY (1998)
JOURNAL OF THEORETICAL PROBABILITY 11(3): 715-731.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We estimate the concentration functions of n-fold convolutions of one-dimensional probability measures. The Kolmogorov-Rogozin inequality implies that for nondegenerate distributions these functions decrease at least as O(n(-1/2)). On the other hand, Esseen((3)) has shown that this rate is o(n(-1/2)) iff the distribution has an infinite second moment. This statement was sharpened by Morozova.((9)) Theorem 1 of this paper provides an improvement of Morozova's result. Moreover, we present more general estimates which imply the rates o(n(-1/2)).
Stichworte
concentration functions; rates of decay; n-fold convolutions; sums of iid random variables
Erscheinungsjahr
1998
Zeitschriftentitel
JOURNAL OF THEORETICAL PROBABILITY
Band
11
Ausgabe
3
Seite(n)
715-731
ISSN
0894-9840
Page URI
https://pub.uni-bielefeld.de/record/1625190

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Götze F, Zaitsev AY. Estimates for the rapid decay of concentration functions of n-fold convolutions. JOURNAL OF THEORETICAL PROBABILITY. 1998;11(3):715-731.
Götze, F., & Zaitsev, A. Y. (1998). Estimates for the rapid decay of concentration functions of n-fold convolutions. JOURNAL OF THEORETICAL PROBABILITY, 11(3), 715-731. https://doi.org/10.1023/A:1022654631571
Götze, F., and Zaitsev, A. Y. (1998). Estimates for the rapid decay of concentration functions of n-fold convolutions. JOURNAL OF THEORETICAL PROBABILITY 11, 715-731.
Götze, F., & Zaitsev, A.Y., 1998. Estimates for the rapid decay of concentration functions of n-fold convolutions. JOURNAL OF THEORETICAL PROBABILITY, 11(3), p 715-731.
F. Götze and A.Y. Zaitsev, “Estimates for the rapid decay of concentration functions of n-fold convolutions”, JOURNAL OF THEORETICAL PROBABILITY, vol. 11, 1998, pp. 715-731.
Götze, F., Zaitsev, A.Y.: Estimates for the rapid decay of concentration functions of n-fold convolutions. JOURNAL OF THEORETICAL PROBABILITY. 11, 715-731 (1998).
Götze, Friedrich, and Zaitsev, AY. “Estimates for the rapid decay of concentration functions of n-fold convolutions”. JOURNAL OF THEORETICAL PROBABILITY 11.3 (1998): 715-731.

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