Asymptotic Behavior of Convolution of Dependent Random Variables with Heavy-Tailed Distributions

V. Ranjbar.Y, Mohammad Amini, A. Bozorgnia

Abstract

In this paper, we study the asymptotic behavior of the tail of X1+X2 in a dependent framework; where X1 and X2 are two positive heavy-tailed random variables with continuous joint and common marginal distribution functions F(x, y) and F(x), respectively; and for some classes of heavy-tailed distributions, we obtain some bounds and convolution properties. Furthermore, we prove P(|X1 − X2| > x) a.P(|X| > x) as $x\rightarrow\infty$, where a is a constant and X1, X2 are dependent random variables.