A Skorohod representation and an invariance principle for sums of weighted i.i.d. random variables
A Skorokhod representation is obtained for partial sums \(S_ n=\sum_{i=1}^ n a_ i X_ i\) of weighted i.i.d. r.v.s \(\{X_ i\), \(i\geq 1\}\) with \(E X_ 1=0\) and \(E X_ 1^ 2=1\) and weights \(\{a_ i\), \(i\geq 1\}\). This result enables the author to establish a functional LIL and an almost sure invariance principle for the weighted i.i.d. sequence under consideration.
scientific article; zbMATH DE number 61925
scientific article