THE DOMAIN OF ATTRACTION OF THE OPERATOR FOR TYPE-II AND TYPE-III DISTRIBUTIONS

Let (Y-n) be a sequence of independent random variables with common di stribution F and define the iteration: X-0 = x(0), X-n:= Xn-1 boolean OR (alpha Xn-1 + Y-n), alpha is an element of [0, 1). We denote by D(P hi(y)) the domain of maximal attraction of Phi(y), the extreme value d istribution of the first type. Greenwood and Hooghiemstra showed in 19 91 that for F is an element of D(Phi(y)) there exist norming constants a(n) > 0 and b(n) is an element of R such that a(n)(-1){X-n - b(n)/(1 - alpha)} has a non-degenerate (distributional) limit. In this paper we show that the same is true for F is an element of D(Psi(y)) boolean OR D(boolean AND), the type II and type III domains. The method of pr oof is entirely different from the method in the aforementioned paper. After a proof of tightness of the involved sequences we apply (modify ) a result of Donnelly, concerning weak convergence of Markov chains w ith an entrance boundary.