Limit theorems for maxima of certain dependent random sums / T. V. Kuznetsova. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 3. P. 18-23 [Moscow Univ. Math. Bulletin. Vol. 67, N 3, 2012.].
A family of extrema having form Ymn=max(i≤m)∑(j≤n)Xij, m, n ≥ 1 is considered, here the random variables {Xij}, i≥1, j≥1, are dependent by columns (with identical j) and independent by rows (with different j). The asymptotics of Ymn for m, n → ∞ is studied. Three particular cases are considered: a normal distribution, a Laplace distribution, and an α-stable distribution.
Key words: maxima, random sums, α-stable distribution, Frechet distribution.