Limit theorems for maxima of some dependent random sums (Q355270)

Let \(\{X_{1j}:\,j\in\mathbb N\},\{X_{2j}:\,j\in\mathbb N\},\dots\) be independent sets of (possibly dependent) random variables in each set. Set \(Y_{mn}:=\max_{1\leq i\leq m}\sum_{j=1}^nX_{ij}\). The limit distribution of \(Y_{mn}\), linearly standardized, as \(m,n\to\infty\), is well-known if the random variables \(X_{ij}\), \(i,j\in\mathbb N\), are independent and identically distributed. This paper establishes the limit distribution of \(Y_{mn}\) under particular models for the joint distribution \((X_{i1},\dots,X_{ij})\), \(i,j\in\mathbb N\).