Some results on dependent random variables and a connection with the multivariate s-increasing convex order

ABSTRACT

In this paper, some new concepts of dependence are introduced that generalize the concepts of positive and negative association. The new concepts of dependence are linked to the multivariate s-increasing convex order. Furthermore, a Kolmogorov-type inequality and a Hàjek–Rènyi inequality are proven that lead to an asymptotic result for these new random objects.

KEYWORDS:

• Hàjek–Rènyi inequality
• Kolmogorov-type inequality
• multivariate s-increasing convex order
• negative association
• positive association

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E15
• 60F15