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
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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},
year = {2012},
volume = {18},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/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