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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2025-02-01
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| 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. |
| format | Article |
| id | doaj-art-226cff0db741432f9d286bedbc8b8339 |
| institution | OA Journals |
| issn | 2351-6046 2351-6054 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | VTeX |
| record_format | Article |
| 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 |