---
res:
bibo_abstract:
- 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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Yu. V.
foaf_name: Prokhorov, Yu. V.
foaf_surname: Prokhorov
- foaf_Person:
foaf_givenName: Friedrich
foaf_name: Götze, Friedrich
foaf_surname: Götze
foaf_workInfoHomepage: http://www.librecat.org/personId=10518
- foaf_Person:
foaf_givenName: V. V.
foaf_name: Ulyanov, V. V.
foaf_surname: Ulyanov
bibo_doi: 10.1137/S0040585X97T988514
bibo_issue: '1'
bibo_volume: 62
dct_date: 2018^xs_gYear
dct_identifier:
- UT:000432323500008
dct_isPartOf:
- http://id.crossref.org/issn/0040-585X
- http://id.crossref.org/issn/1095-7219
dct_language: eng
dct_publisher: Siam Publications@
dct_subject:
- powers of random variables
- bounds for characteristic functions
- the
- Vinogradov mean value theorem
- stochastic generalization
dct_title: ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL
VARIABLES@
...