Geodesic
Limit theorems for maxima of some dependent random sums
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2012), pp. 18-23 
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/
@article{VMUMM_2012_3_a3,
     author = {T. V. Kuznetsova},
     title = {Limit theorems for maxima of some dependent random sums},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {18--23},
     year = {2012},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_3_a3/}
}
TY  - JOUR
AU  - T. V. Kuznetsova
TI  - Limit theorems for maxima of some dependent random sums
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2012
SP  - 18
EP  - 23
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2012_3_a3/
LA  - ru
ID  - VMUMM_2012_3_a3
ER  - 
%0 Journal Article
%A T. V. Kuznetsova
%T Limit theorems for maxima of some dependent random sums
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2012
%P 18-23
%N 3
%U http://geodesic.mathdoc.fr/item/VMUMM_2012_3_a3/
%G ru
%F VMUMM_2012_3_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Lebedev A.V., “Predelnye teoremy dlya maksimumov nezavisimykh sluchainykh summ”, Teoriya veroyatn. i ee primen., 44:3 (1999), 631–634 | DOI | MR

[2] Lebedev A.V., “Maksimumy nezavisimykh summ v sluchae tyazhelykh khvostov”, Teoriya veroyatn. i ee primen., 49:4 (2004), 791–794 | DOI

[3] Kuznetsova T.V., “Utochnenie predelnoi teoremy dlya maksimumov nezavisimykh sluchainykh summ v sluchae nulevoi asimmetrii”, Teoriya veroyatn. i ee primen., 55:2 (2010), 357–362 | DOI

[4] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1984 | MR

[5] Borak S., Hardle W., Weron R., Stable distributions, http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2005-008.pdf