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2006 Measure Concentration for Compound Poisson Distributions
Ioannis Kontoyiannis, Mokshay Madiman
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Electron. Commun. Probab. 11: 45-57 (2006). DOI: 10.1214/ECP.v11-1190


We give a simple development of the concentration properties of compound Poisson measures on the nonnegative integers. A new modification of the Herbst argument is applied to an appropriate modified logarithmic-Sobolev inequality to derive new concentration bounds. When the measure of interest does not have finite exponential moments, these bounds exhibit optimal {em polynomial} decay. Simple new proofs are also given for earlier results of Houdr{'e} (2002) and Wu (2000).


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Ioannis Kontoyiannis. Mokshay Madiman. "Measure Concentration for Compound Poisson Distributions." Electron. Commun. Probab. 11 45 - 57, 2006.


Accepted: 9 May 2006; Published: 2006
First available in Project Euclid: 4 June 2016

zbMATH: 1112.60008
MathSciNet: MR2219345
Digital Object Identifier: 10.1214/ECP.v11-1190

Primary: 60E07
Secondary: ‎39B62 , 46N30 , 60E15

Keywords: Compound Poisson measure , entropy method , Herbst argument , logarithmic-Sobolev inequality , measure concentration , polynomial tails

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