Geodesic
Limit theorems for the maximal random sums
Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 3, pp. 520-532

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Necessary and sufficient conditions are given for monotone sequences of scaled random variables with a random index to converge weakly or converge weakly with the mixing property in Rényi's sense. The main results are related with the case when the terms of the sequences are sequential maximal sums of independent random variables.
Keywords: weak convergence, mixing property in Rényi's sense, random variable.
Mots-clés : maximalsum of random variables 
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     author = {V. M. Kruglov and Zhang Bo},
     title = {Limit theorems for the maximal random sums},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {520--532},
     publisher = {mathdoc},
     volume = {41},
     number = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1996_41_3_a2/}
}
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V. M. Kruglov; Zhang Bo. Limit theorems for the maximal random sums. Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 3, pp. 520-532. http://geodesic.mathdoc.fr/item/TVP_1996_41_3_a2/