Sufficient conditions for the subexponential property of the convolution of two distributions

Conditions on the distributions of two independent nonnegative random variablesX andY are given for the sumX+Y to have a subexponential distribution, i.e., (1−F ^(2*)(t))/(1−F(t)) → 2 ast → +∞, whereF(t)=P{X+Y≤t} andF ^(2*)(t) is the convolution ofF(t) with itself. Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 778–781, November, 1995.