Almost Sure Stability of Partial Sums of Uniformly Bounded Random VariablesProceedings of the American Mathematical Society
AbstractSuppose a1 , a2 ,... is a sequence of real numbers with an → ∞. If lim sup(X1+ ... + Xn)/an = α a.s. for every sequence of independent nonnegative uniformly bounded random variables X1,X2,... satisfying some hypothesis condition A, then for every (arbitrarily-dependent) sequence of nonnegative uniformly bounded random variables Y1,Y2, ... , lim sup(Y1+ ... + Yn)/an = α a.s. on the set where the conditional distributions (given the past) satisfy precisely the same condition A. If, in addition, Σ∞a-2n < ∞ , then the assumption of nonnegativity may be dropped.
Citation InformationTheodore P. Hill. "Almost Sure Stability of Partial Sums of Uniformly Bounded Random Variables" Proceedings of the American Mathematical Society Vol. 89 Iss. 4 (1983) p. 685 - 690
Available at: http://works.bepress.com/tphill/57/