Limit theorems for sums of dependent random variables

Abstract

In Lai and Stout [7] the upper half of the law of the iterated logarithm (LIL) is established for sums of strongly dependent stationary Gaussian random variables. Herein, the upper half of the LIL is established for strongly dependent random variables {Xi} which are however not necessarily Gaussian. Applications are made to multiplicative random variables and to ∑f(Zi) where the Ziare strongly dependent Gaussian. A maximal inequality and a Marcinkiewicz-Zygmund type strong law are established for sums of strongly dependent random variables Xisatisfying a moment condition of the form E|Sa,n|p≦g(n), where {Mathematical expression}, generalizing the work of Serfling [13, 14]. © 1980 Springer-Verlag.