We characterize the second order subexponentiality of an infinitely divisible distribution on the real line under an exponential moment assumption. We investigate the asymptotic behaviour of the difference between the tails of an infinitely divisible distribution and its Lévy measure. Moreover, we study the second order asymptotic behaviour of the tail of the $t$th convolution power of an infinitely divisible distribution. The density version for a self-decomposable distribution on the real line without an exponential moment assumption is also given. Finally, the regularly varying case for a self-decomposable distribution on the half line is discussed.

中文翻译：

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二阶次幂和无限可分性

我们在指数矩假设下刻画了实线上无限可分分布的二阶次指数性。我们研究了无限可分分布的尾部与其 Lévy 测度之间的差异的渐近行为。此外，我们研究了无限可分分布的第t次卷积幂尾部的二阶渐近行为。还给出了没有指数矩假设的实线上自分解分布的密度版本。最后，讨论了半线上自分解分布的规律变化情况。