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.

中文翻译：

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半线上无限可分分布的次指数密度

我们证明，在归一化 L\'evy 测度密度的长尾下，半线上无限可分分布的密度是次指数的，当且仅当它们的归一化 L\'evy 测度的密度是次指数的。此外，我们证明，在某个连续性假设下，半线上的无限可分分布的密度是次指数的，当且仅当它们的归一化 L\'evy 测度是局部次指数的。