Subexponential Densities of Infinitely Divisible Distributions on the Half-Line

We show that, under the long-tailedness of the densities of normalized Levy measures, the densities of infinitely divisible distributions on the half-line are subexponential if and only if the densities of their normalized Levy 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 Levy measures are locally subexponential.