A stroll along the gamma

Benjamin Arras and Yvik Swan

Stochastic Processes and their Applications, 2017, vol. 127, issue 11, 3661-3688

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.

Keywords: De Bruijn identity; Entropy; Fisher information; Gamma approximation; Semigroup interpolation; Smart path; Representation formulae (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:11:p:3661-3688

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DOI: 10.1016/j.spa.2017.03.012

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