Measure Concentration for Compound Poisson Distributions
Probability
2024-05-07 v1
Abstract
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 polynomial decay. Simple new proofs are also given for earlier results of Houdr{\'e} (2002) and Wu (2000).
Cite
@article{arxiv.math/0506435,
title = {Measure Concentration for Compound Poisson Distributions},
author = {I. Kontoyiannis and M. Madiman},
journal= {arXiv preprint arXiv:math/0506435},
year = {2024}
}
Comments
12 pages