A new quantitative central limit theorem on the Wiener space with applications to Gaussian processes

Tobias Fissler; Christoph Thaele

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arXiv · 1610.01456

A new quantitative central limit theorem on the Wiener space with applications to Gaussian processes

Tobias Fissler·Christoph Thaele

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Abstract

Quantitative limit theorems for non-linear functionals on the Wiener space are considered. Given the possibly infinite sequence of kernels of the chaos decomposition of such a functional, an estimate for different probability distances between the functional and a Gaussian random variable in terms of contraction norms of these kernels is derived. The applicability of this result is demonstrated by means of the Breuer-Major theorem, unfolding thereby a new connection between the Hermite rank of the considered function and a chaotic gap. Especially, power variations of the fractional Brownian motion and processes belonging to the Cauchy class are studied.

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Tobias Fissler, Christoph Thaele. 2016-10-05. A new quantitative central limit theorem on the Wiener space with applications to Gaussian processes. https://arxiv.org/abs/1610.01456

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