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.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Prokhorov, Yu. V.; Götze, FriedrichUniBi; Ulyanov, V. V.
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.
Stichworte
powers of random variables; bounds for characteristic functions; the; Vinogradov mean value theorem; stochastic generalization
Erscheinungsjahr
2018
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
0040-585X
eISSN
1095-7219
Page URI
https://pub.uni-bielefeld.de/record/2920354

Zitieren

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.