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Moderate deviations on poisson chaos
Citation Link: https://doi.org/10.15480/882.13887
Publikationstyp
Journal Article
Date Issued
2024
Sprache
English
Author(s)
TORE-DOI
Volume
29
Article Number
146
Citation
Electronic Journal of Probability 29: 146 (2024)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Univ. of Washington, Mathematics Dep.
This paper deals with U-statistics of Poisson processes and multiple Wiener-Itô integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variables, moderate deviation principles, concentration inequalities and normal approximation bounds with Cramér correction are derived. It is argued that the results obtained in this way are in a sense best possible and cannot be improved systematically. Applications in stochastic geometry and to functionals of OrnsteinUhlenbeck-Lévy processes are investigated.
Subjects
cumulants | moderate deviations | multiple stochastic integrals | Poisson processes | stochastic geometry | U-statistics
DDC Class
519: Applied Mathematics, Probabilities
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24-EJP1206.pdf
Type
Main Article
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613 KB
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