Functional Gaussian approximations in Hilbert spaces: the non-diffusive case
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Bourguin, Solesne
Campese, Simon
Dang, Thanh
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Citation
Solesne Bourguin, Simon Campese, Thanh Dang. "Functional Gaussian approximations in Hilbert spaces: the non-diffusive case." https://arxiv.org/abs/2110.04877v1
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 nondegenerate
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.
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Attribution-NonCommercial-NoDerivatives 4.0 International