TY - JOUR
AB - 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.
AU - Prokhorov, Yu. V.
AU - GĂ¶tze, Friedrich
AU - Ulyanov, V. V.
ID - 2920354
IS - 1
JF - THEORY OF PROBABILITY AND ITS APPLICATIONS
KW - powers of random variables
KW - bounds for characteristic functions
KW - the
KW - Vinogradov mean value theorem
KW - stochastic generalization
SN - 0040-585X
TI - ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES
VL - 62
ER -