On the fluctuations of independent copies of moving maxima

Abstract

Let (Xn, n?1) be a sequence of independent random variables (r.v.'s) with a common distribution function (d.f.) F. Define the moving maxima Yk(n)=max(Xn-k(n)+1, Xn-k(n)+2.,., X n), where (k(n), n?1) is a sequence of positive integers. Let Yk(n)1 and Yk(n)2 be two independent copies of Yk(n). Under certain conditions on F and k(n), the set of almost sure limit points of the vector consisting of properly normalised Yk(n)1 and Yk(n)2 is obtained. © 2000 Elsevier Science B.V.