Subexponential densities of infinitely divisible distributions on the half line

Abstract: We show that, under the long-tailedness of the densities of normalized L\'evy measures, the densities of infinitely divisible distributions on the half line are subexponential if and only if the densities of their normalized L\'evy measures are subexponential. Moreover, we prove that, under a certain continuity assumption, the densities of infinitely divisible distributions on the half line are subexponential if and only if their normalized L\'evy measures are locally subexponential.