A strong approximation theorem for positively dependent Gaussian sequences and its applications

Abstract: Under the polynomial decay rates and finite second moment, a strong approximation theorem for partial sums of linear positive quadrant dependent Gaussian sequences is derived. As applications, the law of the iterated logarithm, the Chung-type law of the iterated logarithm and the almost sure central limit theorem are obtained with minimal conditions. [Copyright &y& Elsevier]