A quantitative CLT on a finite sum of Wiener chaoses and applications to ratios of Gaussian functionals

Khalifa Es-Sebaiy

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arXiv · 2412.16991

A quantitative CLT on a finite sum of Wiener chaoses and applications to ratios of Gaussian functionals

Khalifa Es-Sebaiy

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Abstract

In this paper we provide a new explicit bound on the total variation distance between a standardized partial sum of random variables belonging to a finite sum of Wiener chaoses and a standard normal random variable. We apply our result to derive an upper bound for the Kolmogorov distance between a ratio of multiple stochastic integrals and a Gaussian random variable.

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BibTeX RIS

Khalifa Es-Sebaiy. 2024-12-22. A quantitative CLT on a finite sum of Wiener chaoses and applications to ratios of Gaussian functionals. https://arxiv.org/abs/2412.16991

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