A functional law of the iterated logarithm for associated sequences
Recently a functional central limit theorem has been demonstrated for classes of associated random variables in a paper of \textit{C. M. Newman} and \textit{A. L. Wright}, Ann. Probab. 9, 671-675 (1981; Zbl 0465.60009). This paper provides certain useful inequalities on the joint characteristic function of normalized partial sums of associated random variables. The results of \textit{I. Berkes} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 26, 246-258 (1973; Zbl 0246.60020)] yield a functional law of the iterated logarithm for sequences of dependent random variables satisfying a condition on joint characteristic functions. These two results, and some calculations, are combined in the current paper to establish a functional law of the iterated logarithm for associated sequences. The rate at which the variance of the properly normalized partial sums approaches its limit is assumed to be polynomial.
functional law of the iterated logarithm
scientific article; zbMATH DE number 3925888