Reference : Optimal Convergence Rates and One-Term Edgeworth Expansions for Multidimensional Func...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Optimal Convergence Rates and One-Term Edgeworth Expansions for Multidimensional Functionals of Gaussian Fields
Campese, Simon mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
ALEA: Latin American Journal of Probability and Mathematical Statistics
Yes (verified by ORBilu)
[en] Malliavin calculus ; Stein's method ; Gaussian approximation ; Edgeworth expanison ; optimality ; multiple integrals
[en] We develop techniques for determining the exact asymptotic speed of convergence in the multidimensional normal approximation of smooth functions of Gaussian fields. As a by-product, our findings yield exact limits and often give rise to one-term generalized Edgeworth expansions increasing the speed of convergence. Our main mathematical tools are Malliavin calculus, Stein's method and the Fourth Moment Theorem. This work can be seen as an extension of the results of arXiv:0803.0458 to the multi-dimensional case, with the notable difference that in our framework covariances are allowed to fluctuate. We apply our findings to exploding functionals of Brownian sheets, vectors of Toeplitz quadratic functionals and the Breuer-Major Theorem.

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