Geodesic
Weak Convergence of Random Sums
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 28-49

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Weak convergence of nonrandomly centered sums of independent random variables with a random number of summands is investigated under the assumption that the number of summands and the summands themselves are independent and the summands are uniformly asymptotically negligible. The theorems proved in this paper are analogues of well-known limit theorems for sums of independent random variables with a nonrandom number of summands.
Keywords: weak convergence, weak compactness, convergence in probability, random sum, distribution function, characteristic function. 
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     author = {V. M. Kruglov and B. Zhang},
     title = {Weak {Convergence} of {Random} {Sums}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a1/}
}
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V. M. Kruglov; B. Zhang. Weak Convergence of Random Sums. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 28-49. http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a1/