Geodesic
Limit theorems for maxima of independent random sums
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 3, pp. 631-633

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We consider extrema of the form $$ Y_{mn}=\max\limits_{1\le i\le m}\sum^n_{j=1}X_{ij},\quad m,n\ge 1, $$ where $X_{ij}$, $i,j\ge 1$, are independent identically distributed random variables. An asymptotic behavior of $Y_{mn}$ as ${m,n\to\infty}$ is investigated. In particular, the paper shows when the asymptotic behavior of $Y_{mn}$ coincides with the asymptotics of maxima of normally distributed variables under some linear normalizing.
Mots-clés : maxima
Keywords: random sums, limit theorems, asymptotic normality, Edgeworth expansion, matrix norms. 
@article{TVP_1999_44_3_a7,
     author = {A. V. Lebedev},
     title = {Limit theorems for maxima of independent random sums},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {631--633},
     publisher = {mathdoc},
     volume = {44},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a7/}
}
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A. V. Lebedev. Limit theorems for maxima of independent random sums. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 3, pp. 631-633. http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a7/