Schulte, MatthiasMatthiasSchulteThäle, ChristophChristophThäle2024-12-112024-12-112024Electronic Journal of Probability 29: 146 (2024)https://hdl.handle.net/11420/52425This 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.en1083-64892024Univ. of Washington, Mathematics Dep.https://creativecommons.org/licenses/by/4.0/cumulants | moderate deviations | multiple stochastic integrals | Poisson processes | stochastic geometry | U-statisticsNatural Sciences and Mathematics::519: Applied Mathematics, ProbabilitiesJournal Articlehttps://doi.org/10.15480/882.1388710.1214/24-EJP120610.15480/882.138872304.00876v2Journal Article