Concentration on Poisson spaces via modified Φ-Sobolev inequalities

Anna Gusakova, Holger Sambale and Christoph Thäle

Stochastic Processes and their Applications, 2021, vol. 140, issue C, 216-235

Abstract: Concentration properties of functionals of general Poisson processes are studied. Using a modified Φ-Sobolev inequality a recursion scheme for moments is established, which is of independent interest. This is applied to derive moment and concentration inequalities for functionals on abstract Poisson spaces. Applications of the general results in stochastic geometry, namely Poisson cylinder models and Poisson random polytopes, are presented as well.

Keywords: Concentration inequalities; Lp-estimates; Modified Φ-Sobolev inequalities; Poisson processes; Stochastic geometry (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.06.009

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