Geodesic
On the convergence of~distributions of~random sums of~independent random variables to~stable laws
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 4, pp. 818-820

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The paper gives the necessary and sufficient conditions for convergence of distributions of random sums of independent random variables to strictly stable laws.
Keywords: stable laws, Lindeberg condition, random sums. 
@article{TVP_1997_42_4_a11,
     author = {V. Yu. Korolev},
     title = {On the convergence of~distributions of~random sums of~independent random variables to~stable laws},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {818--820},
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_4_a11/}
}
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V. Yu. Korolev. On the convergence of~distributions of~random sums of~independent random variables to~stable laws. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 4, pp. 818-820. http://geodesic.mathdoc.fr/item/TVP_1997_42_4_a11/