Abstract: In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The characterizations obtained in the paper represent joint distributions of dependent random variables and their copulas as sums of U -statistics in independe...

Let {Xn, n ≥ 1} be a sequence of negatively superadditive dependent random variables. In the paper, we study the strong law of large numbers for general weighted sums 1 g(n) ∑n i=1 Xi h(i) of negatively superadditive dependent random variables with non-identical distribution. Some sufficient conditions for the strong law of large numbers are provided. As applications, the Kolmogorov strong law ...

We estimate Value-at-Risk for sums of dependent random variables. We model multivariate dependent random variables using archimedean copulas. This structure allows one to calculate the asymptotic behaviour of extremal events. An important application of such results are Value-at-Risk estimates for sums of dependent random variables.

ABSTRACT: In this paper, the complete convergence and the complete moment convergence of weighted sums for an array of negatively superadditive dependent random variables are established. The results generalize the Baum-Katz theorem on negatively superadditive dependent random variables. In particular, the Marcinkiewicz-Zygmund type strong law of large numbers of weights sums for sequences of n...