Geodesic
On Convergence of Random Sums of Random Variables to the Normal Law
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 2, pp. 380-382

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In this paper, sums of a random number of independent random symmetric variables with the same distribution are investigated. Necessary and sufficient conditions for convergence of these sums to the normal law are given. 
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     author = {A. V. Pechinkin},
     title = {On {Convergence} of {Random} {Sums} of {Random} {Variables} to the {Normal} {Law}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {380--382},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_2_a16/}
}
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A. V. Pechinkin. On Convergence of Random Sums of Random Variables to the Normal Law. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 2, pp. 380-382. http://geodesic.mathdoc.fr/item/TVP_1973_18_2_a16/