We show the convolution equivalence property of univariate tempered stable distributions in the sense of Rosiński (2007). This makes rigorous various classic heuristic arguments on the asymptotic similarity between the probability and Lévy densities of such distributions. Some specific examples from the literature are discussed.

中文翻译：

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实线上缓和稳定分布的卷积等价

我们展示了 Rosiński (2007) 意义上的单变量调节稳定分布的卷积等价性。这使得关于此类分布的概率和莱维密度之间的渐近相似性的各种经典启发式论证变得严格。讨论了文献中的一些具体例子。