Geodesic
A new asymptotic expansion and asymptotically best constants in Lyapunov's theorem. III
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 475-497 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A new asymptotic expansion is obtained in Lyapunov's central limit theorem for distribution functions of centered and normed sums of independent random variables which are not necessary identically distributed. It is applied to determine the asymptotically best constants in the Berry–Esseen inequality, thus solving problems of their optimal values raised by Kolmogorov and Zolotarev.
Keywords: central limit theorem, Lyapunov's theorem, Berry–Esseen bounds, asymptotic expansion, characteristic functions. 
@article{TVP_2002_47_3_a2,
     author = {G. P. Chistyakov},
     title = {A new asymptotic expansion and asymptotically best constants in {Lyapunov's} {theorem.~III}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {475--497},
     year = {2002},
     volume = {47},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a2/}
}
TY  - JOUR
AU  - G. P. Chistyakov
TI  - A new asymptotic expansion and asymptotically best constants in Lyapunov's theorem. III
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2002
SP  - 475
EP  - 497
VL  - 47
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a2/
LA  - ru
ID  - TVP_2002_47_3_a2
ER  - 
%0 Journal Article
%A G. P. Chistyakov
%T A new asymptotic expansion and asymptotically best constants in Lyapunov's theorem. III
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2002
%P 475-497
%V 47
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a2/
%G ru
%F TVP_2002_47_3_a2
G. P. Chistyakov. A new asymptotic expansion and asymptotically best constants in Lyapunov's theorem. III. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 475-497. http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a2/