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Modern Stochastics: Theory and Applications


Approximations related to tempered stable distributions
Pub. online: 27 February 2025      Type: Research Article      Open accessOpen Access
Received
14 August 2024
Revised
24 January 2025
Accepted
15 February 2025
Published
27 February 2025

Abstract

In this article, we first obtain, for the Kolmogorov distance, an error bound between a tempered stable and a compound Poisson distribution (CPD) and also an error bound between a tempered stable and an α-stable distribution via Stein’s method. For the smooth Wasserstein distance, an error bound between two tempered stable distributions (TSDs) is also derived. As examples, we discuss the approximation of a TSD to normal and variance-gamma distributions (VGDs). As corollaries, the corresponding limit theorem follows.

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© 2025 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
Probability approximations tempered stable distributions stable distributions Stein’s method characteristic function approach

MSC2020
62E17 (primary) 62E20 (primary) 60E05 (secondary) 60E07 (secondary)

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