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.
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/
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[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