Measure Concentration for Compound Poisson Distributions

Details Measure Concentration for Compound Poisson Distributions Measure Concentration for Compound Poisson Distributions

2005-06-21

arxiv.org/abs/math/0506435v1

Electronic Communications in Probability, 11, pp. 45-57, 2006

Mathematics

Probability

12 pages

Scientific paper

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).

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