On the convolution equivalence of tempered stable distributions on the real line
We show the convolution equivalence property of univariate tempered stable distributions in the sense of Rosinsky (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.
Area: CS49 - Analytical and numerical methods for energy transition (Tiziano Vargiolu and Athena Picarelli)
Keywords: Tempered stable distributions, convolution equivalence, subexponentiality, long tails, heavy tails
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