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A stroll along the gamma

Author

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  • Arras, Benjamin
  • Swan, Yvik

Abstract

We provide the first in-depth study of the Laguerre interpolation scheme between an arbitrary probability measure and the gamma distribution. We propose new explicit representations for the Laguerre semigroup as well as a new intertwining relation. We use these results to prove a local De Bruijn identity which hold under minimal conditions. We obtain a new proof of the logarithmic Sobolev inequality for the gamma law with α≥1/2 as well as a new type of HSI inequality linking relative entropy, Stein discrepancy and standardized Fisher information for the gamma law with α≥1/2.

Suggested Citation

  • Arras, Benjamin & Swan, Yvik, 2017. "A stroll along the gamma," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3661-3688.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:11:p:3661-3688
    DOI: 10.1016/j.spa.2017.03.012
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    Cited by:

    1. Decreusefond, Laurent & Halconruy, Hélène, 2019. "Malliavin and Dirichlet structures for independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2611-2653.

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