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- W4366196534 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." @default.
- W4366196534 created "2023-04-19" @default.
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- W4366196534 date "2021-10-10" @default.
- W4366196534 modified "2023-09-23" @default.
- W4366196534 title "Functional Gaussian approximations on Hilbert-Poisson spaces" @default.
- W4366196534 doi "https://doi.org/10.48550/arxiv.2110.04877" @default.
- W4366196534 hasPublicationYear "2021" @default.
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