Journal of the
Korean Mathematical Society JKMS

We derive the almost sure convergence for weighted sums of random variables which are either pairwise positive quadrant dependent or pairwise negative quadrant dependent and then apply this result to obtain the almost sure convergence of weighted averages. We also extend some results on the strong law of large numbers for pairwise independent identically distributed random variables established in Petrov to the weighted sums of pairwise negative quadrant dependent random variables.

Keywords: pairwise positive quadrant dependent, pairwise negative quadrant dependent, almost sure convergence, weighted sums

MSC numbers: 60F15, 60F99