Stein's method and a quantitative Lindeberg CLT for the Fourier transforms of random vectors

Abstract

We use a multivariate version of Stein's method to establish a quantitative Lindeberg CLT for the Fourier transforms of random $N$-vectors. We achieve this by deducing a specific integral representation for the Hessian matrix of a solution to the Stein equation with test function $e_t(x)=\exp (-i{\sum }_{k=1}^N{t}_k{x}_k)$, where $t,x\in {\mathbb{R}}^N$.

17 pages

References in corpus (5)

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