Functional Gaussian approximations on Hilbert-Poisson spaces
Probability
2023-04-17 v2 Functional Analysis
Abstract
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.
Cite
@article{arxiv.2110.04877,
title = {Functional Gaussian approximations on Hilbert-Poisson spaces},
author = {Solesne Bourguin and Simon Campese and Thanh Dang},
journal= {arXiv preprint arXiv:2110.04877},
year = {2023}
}