Berry–Esséen bound for complex Wiener–Itô integral

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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Publication Details

Journal
Stochastics and Dynamics
Published
2025-03-01
DOI
https://doi.org/10.1142/s0219493725500133
Primary Topic
Algebraic and Geometric Analysis
Type
article
Field-Weighted Citation Impact
0.00
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article

Berry–Esséen bound for complex Wiener–Itô integral

Yong Chen, Yong Liu, Huiping Chen
Stochastics and Dynamics
Algebraic and Geometric Analysis
article

Berry–Esséen bound for complex Wiener–Itô integral

Yong Chen, Yong Liu, Huiping Chen
article en

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.

Stochastics and DynamicsVol. 25(02)
Chinese Academy of Sciences (CN), Peking University (CN), Jiangxi Science and Technology Normal University (CN), Academy of Mathematics and Systems Science (CN), Baoshan University (CN), Jiangxi Normal University (CN)
Openalex Percentile: Top 92%
Algebraic and Geometric Analysis
DOISourceOpenAlex
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Berry–Esséen bound for complex Wiener–Itô integral — Yong Chen, Yong Liu, et al. · Stochastics and Dynamics (2025) | TGRS Research Map | TGRS