In this paper we obtain based on an idea of M. Knott and C. S. Smith (1994, Linear Algebra Appl.199, 363-371) characterizations of solutions of three-coupling problems by reduction to the construction of optimal couplings of each of the variables to the sum. In the case of normal distributions...

A convergence theorem of Billingsley for the empirical process of stationary, real valued radom variables under a mixing condition is generalized to the k-dimensional and nonstationary case. Further a more general empirical process is treated, including the upper summation boundary as argument....

The dependence concept of weak association is introduced and is shown to be equivalent to positive quadrant dependence. Furthermore, a characterization of independence in the class of positive quadrant dependent random variables by means of moment conditions is proved. Both results generalize...