ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES
Prokhorov, Yu. V.
Götze, Friedrich
Ulyanov, V. V.
powers of random variables
bounds for characteristic functions
the
Vinogradov mean value theorem
stochastic generalization
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.
Siam Publications
2018
info:eu-repo/semantics/article
doc-type:article
text
https://pub.uni-bielefeld.de/record/2920354
Prokhorov YV, Götze F, Ulyanov VV. ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES. <em>THEORY OF PROBABILITY AND ITS APPLICATIONS</em>. 2018;62(1):98-116.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1137/S0040585X97T988514
info:eu-repo/semantics/altIdentifier/issn/0040-585X
info:eu-repo/semantics/altIdentifier/issn/1095-7219
info:eu-repo/semantics/altIdentifier/wos/000432323500008
info:eu-repo/semantics/closedAccess