Geodesic
On the Stein--Tikhomirov method and its applications in nonclassical limit theorems
Diskretnaya Matematika, Tome 19 (2007) no. 1, pp. 27-39

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In this paper we give necessary and sufficient conditions for validity of the central limit theorem for sums of independent random variables in terms of characteristic functions in a nonclassical setup where an essential contribution of individual variables to the sum is allowed. These conditions are formulated with the use of the Stein–Tikhomirov operator. 
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     author = {Sh. K. Formanov},
     title = {On the {Stein--Tikhomirov} method and its applications in nonclassical limit theorems},
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Sh. K. Formanov. On the Stein--Tikhomirov method and its applications in nonclassical limit theorems. Diskretnaya Matematika, Tome 19 (2007) no. 1, pp. 27-39. http://geodesic.mathdoc.fr/item/DM_2007_19_1_a4/