On the convolution equivalence of tempered stable distributions on the real line

Lorenzo Torricelli

Statistics & Probability Letters, 2024, vol. 207, issue C

Abstract: 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.

Keywords: Tempered stable distributions; Convolution equivalence; Subexponentiality; Long tails; Heavy tails (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110034

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