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- W4288357320 abstract "We introduce a framework to derive quantitative central limit theorems in the context of non-linear approximation of Gaussian random variables taking values in a separable Hilbert space. In particular, our method provides an alternative to the usual (non-quantitative) finite dimensional distribution convergence and tightness argument for proving functional convergence of stochastic processes. We also derive four moments bounds for Hilbert-valued random variables with possibly infinite chaos expansion, which include, as special cases, all finite-dimensional four moments results for Gaussian approximation in a diffusive context proved earlier by various authors. Our main ingredient is a combination of an infinite-dimensional version of Stein's method as developed by Shih and the so-called Gamma calculus. As an application, rates of convergence for the functional Breuer-Major theorem are established." @default.
- W4288357320 created "2022-07-29" @default.
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- W4288357320 date "2019-05-13" @default.
- W4288357320 modified "2023-09-23" @default.
- W4288357320 title "Approximation of Hilbert-valued Gaussians on Dirichlet structures" @default.
- W4288357320 doi "https://doi.org/10.48550/arxiv.1905.05127" @default.
- W4288357320 hasPublicationYear "2019" @default.
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