Approximations related to tempered stable distributions

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 bet...

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Main Authors: Kalyan Barman, Neelesh S Upadhye, Palaniappan Vellaisamy
Format: Article
Language:English
Published: VTeX 2025-02-01
Series:Modern Stochastics: Theory and Applications
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Online Access:https://www.vmsta.org/doi/10.15559/25-VMSTA275
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author Kalyan Barman
Neelesh S Upadhye
Palaniappan Vellaisamy
author_facet Kalyan Barman
Neelesh S Upadhye
Palaniappan Vellaisamy
author_sort Kalyan Barman
collection DOAJ
description 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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series Modern Stochastics: Theory and Applications
spelling doaj-art-226cff0db741432f9d286bedbc8b83392025-08-20T02:34:42ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542025-02-0112332534610.15559/25-VMSTA275Approximations related to tempered stable distributionsKalyan Barman0Neelesh S Upadhye1Palaniappan Vellaisamy2Department of mathematics, IIT Bombay, Powai, 400076, IndiaDepartment of Mathematics, IIT Madras, Chennai, 600036, IndiaDepartment of Statistics and Applied Probability, UC Santa Barbara, Santa Barbara, CA, 93106, USAIn 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.https://www.vmsta.org/doi/10.15559/25-VMSTA275Probability approximationstempered stable distributionsstable distributionsStein’s methodcharacteristic function approach
spellingShingle Kalyan Barman
Neelesh S Upadhye
Palaniappan Vellaisamy
Approximations related to tempered stable distributions
Modern Stochastics: Theory and Applications
Probability approximations
tempered stable distributions
stable distributions
Stein’s method
characteristic function approach
title Approximations related to tempered stable distributions
title_full Approximations related to tempered stable distributions
title_fullStr Approximations related to tempered stable distributions
title_full_unstemmed Approximations related to tempered stable distributions
title_short Approximations related to tempered stable distributions
title_sort approximations related to tempered stable distributions
topic Probability approximations
tempered stable distributions
stable distributions
Stein’s method
characteristic function approach
url https://www.vmsta.org/doi/10.15559/25-VMSTA275
work_keys_str_mv AT kalyanbarman approximationsrelatedtotemperedstabledistributions
AT neeleshsupadhye approximationsrelatedtotemperedstabledistributions
AT palaniappanvellaisamy approximationsrelatedtotemperedstabledistributions