English

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

R2 v1 2026-06-28T17:31:52.480Z