Extremal behaviour in models of superposition of random variables

Abstract

Let X(i) ={Xgi(n)}n≥1, i= 1, 2, be sequences of random variables, where {gi(n)}n≥1 are disjoint and strictly increasing sequences of integer numbers such that {g1(n)}n≥1 ∪ {g2(n)}n≥1 = N. Using superposition of point processes, we study the extremal behaviour of a superposed sequence {Xn}n≥1 = {Xg1(n)}n≥1 ∪ {Xg2(n)}n≥1 , where we consider the proportion of variables superposed from each sequence asymptotically constant and {Xn}n≥1 verifying some dependence conditions. We apply the obtained results in the computation of the bivariate extremal index.