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Berry-Esséen bound for complex Wiener-Itô integral
Huiping Chen, Yong Chen, Yong Liu · 2024-07-07 · via math.PR updates on arXiv.org

For complex multiple Wiener-Itô integral, we present Berry-Esséen 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-Esséen bound for a statistic associated with the complex-valued Ornstein-Uhlenbeck process.

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