Suppose {Xn,n≥1} is a stationary sequence satisfying the D and D' mixing conditions given by Adler. Suppose further that g and h are functions on the positive integers such that h is positive, periodic with integer period p≥1 and g satisfies a certain growth rate condition. By first exhibiting the weak convergence of a sequence of point processes related to {g(i)+h(i)Xi,i≥1}, we derive the asymptotic distribution of Mn=ℝnab21iÅ=1(g(i)+h(i)Xi). When {Xn} is in the maximal
