Geodesic
Maxima of independent sums in the presence of
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 791-794

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Let $$Y_{mn}=\max_{1\le i\le m}\sum_{j=1}^n X_{ij},\qquad m,n\ge 1,$$ be a family of extremes, where $X_{ij}$, $i,j\ge 1$, are independent with common subexponential distribution $F$. The limit behavior of $Y_{mn}$ is investigated as $m,n\to\infty$. Various nondegenerate limit laws are obtained (Fréchet and Gumbel), depending on the relative rate of growth of $m,n$ and the tail behavior of $F$.
Mots-clés : maxima
Keywords: sums, regularly varying tails, subexponentiality, nondegenerate limit laws, linear scalingю. 
@article{TVP_2004_49_4_a10,
     author = {A. V. Lebedev},
     title = {Maxima of independent sums in the presence of},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {791--794},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a10/}
}
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A. V. Lebedev. Maxima of independent sums in the presence of. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 791-794. http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a10/