ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES

Prokhorov YV, Götze F, Ulyanov VV (2018)
THEORY OF PROBABILITY AND ITS APPLICATIONS 62(1): 98-116.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We obtain upper bounds for the absolute values of the characteristic functions of the kth powers of asymptotically normal random variables. Estimates are proved for the case when asymptotically normal random variables are normalized sums of independent identically distributed summands with a "regular" distribution. Possible generalizations are considered. The estimates extend the results of previous studies, where for the distributions of the summands, the presence of either a discrete or an absolutely continuous component was required. The proofs of the bounds are based on the stochastic generalization of the I. M. Vinogradov mean value theorem, which is also obtained in the present paper.
Erscheinungsjahr
Zeitschriftentitel
THEORY OF PROBABILITY AND ITS APPLICATIONS
Band
62
Ausgabe
1
Seite(n)
98-116
Konferenz
International Conference on Probability and Statistics
Konferenzort
Moscow, RUSSIA
ISSN
eISSN
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Prokhorov YV, Götze F, Ulyanov VV. ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES. THEORY OF PROBABILITY AND ITS APPLICATIONS. 2018;62(1):98-116.
Prokhorov, Y. V., Götze, F., & Ulyanov, V. V. (2018). ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES. THEORY OF PROBABILITY AND ITS APPLICATIONS, 62(1), 98-116. doi:10.1137/S0040585X97T988514
Prokhorov, Y. V., Götze, F., and Ulyanov, V. V. (2018). ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES. THEORY OF PROBABILITY AND ITS APPLICATIONS 62, 98-116.
Prokhorov, Y.V., Götze, F., & Ulyanov, V.V., 2018. ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES. THEORY OF PROBABILITY AND ITS APPLICATIONS, 62(1), p 98-116.
Y.V. Prokhorov, F. Götze, and V.V. Ulyanov, “ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES”, THEORY OF PROBABILITY AND ITS APPLICATIONS, vol. 62, 2018, pp. 98-116.
Prokhorov, Y.V., Götze, F., Ulyanov, V.V.: ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES. THEORY OF PROBABILITY AND ITS APPLICATIONS. 62, 98-116 (2018).
Prokhorov, Yu. V., Götze, Friedrich, and Ulyanov, V. V. “ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES”. THEORY OF PROBABILITY AND ITS APPLICATIONS 62.1 (2018): 98-116.