Year: 2023
Type: preprint
Abstract: 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 Ornstein-Uhlenbeck-Lévy processes are investigated.
Source: arXiv (Cornell University)
Authors: Schulte, Matthias, Thaele, Christoph
Institution: Hamburg University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G3617462173
OpenAlex ID: W4362598741