The class J of subexponential distributions is characterized by F(0) = 0, 1 - F⁽²⁾ (x) ~ 2\1 - F(x)\ as x → ∞. New properties of the class J are derived as well as for the more general case where 1 - F⁽²⁾ (x) ~ β\1 - F(x)\. An application to transient renewal theory illustrates these results as does an adaptation of a result of Greenwood on randomly stopped sums of subexponentially distributed random variables.
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Jozef L. Teugels (1975) studied this question.