Concentration on Poisson spaces via modified Φ-Sobolev inequalities

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:140

Article

Gusakova, Anna¹  Sambale, Holger²  Thaele, Christoph¹ 

[1] Ruhr Univ Bochum, Fac Math, D-44780 Bochum, Germany

[2] Bielefeld Univ, Fac Math, POB 10 01 31, D-33501 Bielefeld, Germany

关键词: Concentration inequalities;    L-p-estimates;    Modified Phi-Sobolev inequalities;    Poisson processes;    Stochastic geometry;   

DOI  :  10.1016/j.spa.2021.06.009

来源: Elsevier

【 摘 要 】

Concentration properties of functionals of general Poisson processes are studied. Using a modified Phi-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. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free