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. 72, N 2, 2017. P. 0].

A family of extrema having form Ymn=max(im)(jn)Xij, mn ≥ 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.

№ 3/2012