We give a sufficient condition for i.i.d. random variables X1,X2 in order to have P{X1 -X2>x}∼P{ X1 >x}, as x→∞. A factorization property for subexponential distributions is used in the proof.

Convolution, Heavy tails, Subexponentiality, Symmetrization
dx.doi.org/10.1016/j.spl.2004.06.004, hdl.handle.net/1765/66546
Statistics & Probability Letters
Erasmus School of Economics

Geluk, J.L. (2004). Asymptotics in the symmetrization inequality. Statistics & Probability Letters, 69(1), 63–68. doi:10.1016/j.spl.2004.06.004