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Lower variance bounds and normal approximation of Poisson functionals in stochastic geometry
Citation Link: https://doi.org/10.15480/882.13774
Publikationstyp
Doctoral Thesis
Date Issued
2024
Sprache
English
Author(s)
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2024-11-13
Institute
TORE-DOI
Citation
Technische Universität Hamburg (2024)
Lower bounds for variances are often required for deriving central limit theorems. In this thesis, a generalised reverse Poincaré inequality is established, which provides a lower variance bound for Poisson functionals and depends on the difference operator of some fixed order. To show how this lower variance bound can be used, three different applications from stochastic geometry are explored: statistics of spatial random graphs in Euclidean and hyperbolic space, Lp surface areas of random polytopes in the Euclidean unit ball and geometric functionals of excursion sets of Poisson shot noise processes.
Subjects
lower variance bounds
normal approximation
Poisson functionals
Poisson shot noise processes
random polytopes
spatial random graphs
DDC Class
510: Mathematics
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