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.