The subexponentiality of products revisited
نویسندگان
چکیده
Following the work of Cline and Samorodnitsky (Stoch. Process. Their Appl. 49(1):75–98, 1994), we reexamine the subexponentiality of the product of two random variables, X and Y, which are independent and have distributions F and G, respectively. The main result is the following: If F belongs to the class A [that is to say, F is subexponential and lim supx→∞ F(vx)/F(x) < 1 holds for some v > 1] and G, with G(0−) = 0 and G(0) < 0, satisfies G(ux) = o(1)Pr (XY > x) for each u > 0, then the distribution of XY also belongs to the class A.
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