Berry-Ess\'een bound for complex Wiener-It\^{o} integral
Probability
2024-07-09 v1
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.
Cite
@article{arxiv.2407.05353,
title = {Berry-Ess\'een bound for complex Wiener-It\^{o} integral},
author = {Huiping Chen and Yong Chen and Yong Liu},
journal= {arXiv preprint arXiv:2407.05353},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2304.08088