Bourguin, SolesneSolesneBourguinCampese, SimonSimonCampeseDang, ThanhThanhDang2024-06-042024-06-042024Alea (Rio de Janeiro) 21: 517-553 (2024)https://hdl.handle.net/11420/47722We 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.en1980-04362024517553Institute of Mathematical Statistics (Beachwood, Ohio)fourth moment conditionsfunctional limit theoremsGaussian approximationsGaussian measures on Hilbert spacesPoisson spaceStein’s method on Banach spacesNatural Sciences and Mathematics::510: MathematicsJournal Article10.30757/ALEA.v21-21Journal Article