Strong laws of large numbers for pairwise quadrant dependent random variables

For a sequence (X-n, n >= 1} of quadrant dependent random variables satisfying E |X-n| < infinity for all n >= 1 and a family of positive sequences {b(n)), we give sufficient conditions to obtain Sigma(n)(k=1) (X-k - EXk)/b(n) as -> 0. For random sequences which are additionally stochastically dominated by a random variable X is an element of L-p, 1 < p < 2, we shall prove strong laws of large numbers under normalising sequences asymptotically equivalent to n(1/p), 1 < p < 2 up to a logarithm power. (C) 2018 Elsevier B.V. All rights reserved.