On the functional CLT for partial sums of truncated bounded from below random variables

Abstract

Abstract. Let {X, X i } i≥1 be i.i.d. bounded from below continuous random variables, E|X| < ∞, EX 2 = ∞, and {b n } n≥1 be a sequence of increasing positive numbers. When X belongs to the Feller class and b n is such that nP X > b n → ∞ and E(XI X>bn )CLT for the truncated sums S n = P n i=1 X i I X i ≤b n is proved.