Geodesic
Limit theorems for maxima of some dependent random sums
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2012), pp. 18-23

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A family of extrema having form $$ Y_{mn}=\max_{1\le i \le m}\sum_{j=1}^n X_{ij},\qquad m,n\ge1, $$ is considered, here the random variables $\{X_{ij}\}$, $i\ge1$, $j\ge1$, are dependent by columns (with identical $j$) and independent by rows (with different $j$). The asymptotics of $Y_{mn}$ for $m,n\to\infty$ is studied. Three particular cases are considered: a normal distribution, a Laplace distribution, and an $\alpha$-stable distribution. 
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     author = {T. V. Kuznetsova},
     title = {Limit theorems for maxima of some dependent random sums},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
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     number = {3},
     year = {2012},
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T. V. Kuznetsova. Limit theorems for maxima of some dependent random sums. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2012), pp. 18-23. http://geodesic.mathdoc.fr/item/VMUMM_2012_3_a3/