Berry-Esséen bound for complex Wiener-Itô integral

Abstract

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.

arXiv admin note: text overlap with arXiv:2304.08088