Geodesic
On estimation of the maximal probability for sums of lattice random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 4, pp. 842-846

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper deals with the estimation of the maximal probability for sums of independent unimodal symmetric lattice random variable $\xi_k$. The author proves the following inequality $$ \sup_x\mathbf{P}(S_n=x)\le\sqrt{\frac6{\pi}}\frac{p_0}{\sqrt{n(1-p_0^2)}}\bigl(1+\frac{c}{\sqrt{n}}\bigr) $$ where $S_n=\xi_1+\dots+\xi_n, p_0=\sup_x\mathbf{P}(\xi_k-x)$ and $c$ is an absolute constant (one may take $c=2$). 
@article{TVP_1973_18_4_a17,
     author = {N. G. Gamkrelidze},
     title = {On estimation of the maximal probability for sums of lattice random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {842--846},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a17/}
}
TY  - JOUR
AU  - N. G. Gamkrelidze
TI  - On estimation of the maximal probability for sums of lattice random variables
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1973
SP  - 842
EP  - 846
VL  - 18
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a17/
LA  - ru
ID  - TVP_1973_18_4_a17
ER  - 
%0 Journal Article
%A N. G. Gamkrelidze
%T On estimation of the maximal probability for sums of lattice random variables
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1973
%P 842-846
%V 18
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a17/
%G ru
%F TVP_1973_18_4_a17
N. G. Gamkrelidze. On estimation of the maximal probability for sums of lattice random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 4, pp. 842-846. http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a17/