Limit theorems for sums of dependent random variables

Summary 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 {X_i} which are however not necessarily Gaussian. Applications are made to multiplicative random variables and to f(Z_i) where the Z_iare strongly dependent Gaussian. A maximal inequality and a Marcinkiewicz-Zygmund type strong law are established for sums of strongly dependent random variables X_isatisfying a moment condition of the form E¦S_a,n¦^pg(n), where , generalizing the work of Serfling [13, 14].Research supported by the National Science Foundation under grant NSF-MCS-78-09179Research supported by the National Science Foundation under grant NSF-MCS-78-04014