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On Brascamp–Lieb and Poincaré type inequalities for generalized tempered stable distribution

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  • Barman, Kalyan
  • Upadhye, Neelesh S.

Abstract

In this article, we obtain a Stein’s lemma for generalized tempered stable distribution. In particular, we derive a Stein operator for the class generalized tempered stable distributions and discuss its implications on the existing literature. Using this lemma, we obtain Brascamp–Lieb and Poincaré type inequalities for generalized tempered stable distribution.

Suggested Citation

  • Barman, Kalyan & Upadhye, Neelesh S., 2022. "On Brascamp–Lieb and Poincaré type inequalities for generalized tempered stable distribution," Statistics & Probability Letters, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:stapro:v:189:y:2022:i:c:s0167715222001444
    DOI: 10.1016/j.spl.2022.109600
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    References listed on IDEAS

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    1. Chen, Louis H. Y., 1982. "An inequality for the multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 306-315, June.
    2. Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
    3. Robert E. Gaunt, 2020. "Wasserstein and Kolmogorov Error Bounds for Variance-Gamma Approximation via Stein’s Method I," Journal of Theoretical Probability, Springer, vol. 33(1), pages 465-505, March.
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