A Strong Invariance Principle for Associated Sequences of Gaussian Random Variables

In this paper, by applying the Skorohod martingale embedding theorem, we prove a strong invariance principle for an associated sequence of Gaussian random variables under the restrictions that the sequence is Gaussian and the covariance coefficients of the sequence decay with power decay rates. As consequences, the law of the iterated logarithm and Chung's law of the iterated logarithm for associated sequences of Gaussian random variables are obtained.