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Functional Gaussian approximations on Hilbert-Poisson spaces
Publikationstyp
Journal Article
Date Issued
2024
Sprache
English
Author(s)
Journal
Volume
21
Start Page
517
End Page
553
Citation
Alea (Rio de Janeiro) 21: 517-553 (2024)
Publisher DOI
Scopus ID
Publisher
Institute of Mathematical Statistics (Beachwood, Ohio)
We develop a functional Stein-Malliavin method in a non-diffusive Poissonian setting, thus obtaining a) quantitative central limit theorems for approximation of arbitrary non-degenerate Gaussian random elements taking values in a separable Hilbert space and b) fourth moment bounds for approximating sequences with finite chaos expansion. Our results rely on an infinite-dimensional version of Stein’s method of exchangeable pairs combined with the so-called Gamma calculus. Two applications are included: Brownian approximation of Poisson processes in Besov-Liouville spaces and a functional limit theorem for an edge-counting statistic of a random geometric graph.
Subjects
fourth moment conditions
functional limit theorems
Gaussian approximations
Gaussian measures on Hilbert spaces
Poisson space
Stein’s method on Banach spaces
DDC Class
510: Mathematics