English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We develop techniques for determining the exact asymptotic speed ofconvergence in the multidimensional normal approximation of smooth functions ofGaussian fields. As a by-product, our findings yield exact limits and oftengive rise to one-term generalized Edgeworth expansions increasing the speed ofconvergence. Our main mathematical tools are Malliavin calculus, Stein's methodand the Fourth Moment Theorem. This work can be seen as an extension of theresults of arXiv:0803.0458 to the multi-dimensional case, with the notabledifference that in our framework covariances are allowed to fluctuate. We applyour findings to exploding functionals of Brownian sheets, vectors of Toeplitzquadratic functionals and the Breuer-Major Theorem.

Optimal Convergence Rates and One-Term Edgeworth Expansions for Multidimensional Functionals of Gaussian Fields