Limit theorems for sums of dependent random variables

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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 i are strongly dependent Gaussian. A maximal inequality and a Marcinkiewicz-Zygmund type strong law are established for sums of strongly dependent random variables X i satisfying a moment condition of the form E¦S a,n ¦p≦g(n), where \(S_{a,n} = \sum\limits_{a + 1}^{a + n} {X_i }\) , generalizing the work of Serfling [13, 14].

Research supported by the National Science Foundation under grant NSF-MCS-78-09179
Research supported by the National Science Foundation under grant NSF-MCS-78-04014