Moment bounds and central limit theorems for Gaussian subordinated arrays

Jean-Marc Bardet; Donatas Surgailis

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arXiv · 1104.4732

Moment bounds and central limit theorems for Gaussian subordinated arrays

Jean-Marc Bardet·Donatas Surgailis

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Abstract

A general moment bound for sums of products of Gaussian vector's functions extending the moment bound in Taqqu (1977, Lemma 4.5) is established. A general central limit theorem for triangular arrays of nonlinear functionals of multidimensional non-stationary Gaussian sequences is proved. This theorem extends the previous results of Breuer and Major (1981), Arcones (1994) and others. A Berry-Esseen-type bound in the above-mentioned central limit theorem is derived following Nourdin, Peccati and Podolskij (2011). Two applications of the above results are discussed. The first one refers to the asymptotic behavior of a roughness statistic for continuous-time Gaussian processes and the second one is a central limit theorem satisfied by long memory locally stationary process.

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Jean-Marc Bardet, Donatas Surgailis. 2011-04-25. Moment bounds and central limit theorems for Gaussian subordinated arrays. https://arxiv.org/abs/1104.4732

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