On the speed of convergence in the local limit theorem for triangular arrays of random variables
Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 24-32.

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

We establish the upper bound on the speed of convergence to the infinitely divisible limit density in the local limit theorem for triangular arrays of random variables $\{X_{k,n},\, k=1,..,a_n, \, n\in \mathbb{N}\}$.
Keywords: Local limit theorem, infinitely divisible law, speed of convergence.
@article{THSP_2012_18_2_a3,
     author = {V. P. Knopova},
     title = {On the speed of convergence in the local limit theorem for triangular arrays of random variables},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {24--32},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a3/}
}
TY  - JOUR
AU  - V. P. Knopova
TI  - On the speed of convergence in the local limit theorem for triangular arrays of random variables
JO  - Teoriâ slučajnyh processov
PY  - 2012
SP  - 24
EP  - 32
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a3/
LA  - en
ID  - THSP_2012_18_2_a3
ER  - 
%0 Journal Article
%A V. P. Knopova
%T On the speed of convergence in the local limit theorem for triangular arrays of random variables
%J Teoriâ slučajnyh processov
%D 2012
%P 24-32
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a3/
%G en
%F THSP_2012_18_2_a3
V. P. Knopova. On the speed of convergence in the local limit theorem for triangular arrays of random variables. Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 24-32. http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a3/

[1] H. Bateman, A. Erdèlyi, Tables of integral transforms, v. 1, McGraw-Hill, New York, 1954 | Zbl

[2] W. Feller, An Introduction to Probability Theory and Its Applications, v. II, Second edition, John Wiley $\$ Sons, Inc., New York-London-Sydney, 1971 | MR | Zbl

[3] I. A. Ibragimov, Yu. V. Linnik, Independent and stationary dependent variables, Wolters-Nordhoff Publishing, Groningen, 1971 | MR

[4] O. Kallenberg, “Splitting at backward times in regenerative sets”, Ann. Prob., 9 (1981), 781–799 | DOI | MR | Zbl

[5] I. Korchinsky, A. M. Kulik, “Local limit theorem for triangular array of random variables”, Theory Stoch. Proc., 13 (29):3 (2007), 48–54 | MR | Zbl

[6] E. Lukacs, Characteristic function, Griffin, London, 1979