Berry-Ess\'een bound for complex Wiener-It\^{o} integral

Huiping Chen; Yong Chen; Yong Liu

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arXiv · 2407.05353

Berry-Ess\'een bound for complex Wiener-It\^{o} integral

Huiping Chen·Yong Chen·Yong Liu

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Abstract

For complex multiple Wiener-It\^{o} integral, we present Berry-Ess\'een upper and lower bounds in terms of moments and kernel contractions under the Wasserstein distance. As a corollary, we simplify the previously known contraction condition of the complex Fourth Moment Theorem. Additionally, as an application, we explore the optimal Berry-Ess\'een bound for a statistic associated with the complex-valued Ornstein-Uhlenbeck process.

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Huiping Chen, Yong Chen, Yong Liu. 2024-07-07. Berry-Ess\'een bound for complex Wiener-It\^{o} integral. https://arxiv.org/abs/2407.05353

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