Berry-Esseen bound for complex Wiener-Ito integral

被引：0

作者：

Chen, Huiping ^{[1
,2
]}

Chen, Yong ^{[3
,4
]}

Liu, Yong ^{[1
]}

机构：

[1] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[3] Baoshan Univ, Sch Big Data, Baoshan 678000, Yunnan, Peoples R China

[4] Jiangxi Normal Univ, Ctr Appl Math, Sch Math & Stat, Nanchang 330022, Jiangxi, Peoples R China

来源：

STOCHASTICS AND DYNAMICS | 2025年

基金：

中国博士后科学基金;

关键词：

Berry-Esseen bound; complex Wiener-Ito integral; Fourth Moment Theorem; CENTRAL LIMIT-THEOREMS; PARAMETER-ESTIMATION; STEINS METHOD; ASYMPTOTICS; FREQUENCY;

D O I：

10.1142/S0219493725500133

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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

引用

页数：28

共 40 条

[1] Maximum likelihood binary detection in improper complex Gaussian noise [J].

Aghaei, Amirhossein S. ;

Plataniotis, Konstantinos N. ;

Pasupathy, Subbarayan .

2008 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, VOLS 1-12, 2008, :3209-3212

[2] Parameter estimation for the complex fractional Ornstein-Uhlenbeck processes with Hurst parameter H ∈ (0,1/2) [J].

Alazemi, Fares ;

Alsenafi, Abdulaziz ;

Chen, Yong ;

Zhou, Hongjuan .

CHAOS SOLITONS & FRACTALS, 2024, 188

[3] The world of the complex Ginzburg-Landau equation [J].

Aranson, IS ;

Kramer, L .

REVIEWS OF MODERN PHYSICS, 2002, 74 (01) :99-143

[4]

ARATO M, 1962, DOKL AKAD NAUK SSSR+, V146, P747

[5]

Arato M., 1982, Linear Stochastic Systems With Constant Coefficients: A Statistical Approach

[6] On the distribution of poles of Pade approximants to the Z-transform of complex Gaussian white noise [J].

Barone, P .

JOURNAL OF APPROXIMATION THEORY, 2005, 132 (02) :224-240

[7]

Biermé H, 2012, ALEA-LAT AM J PROBAB, V9, P473

[8]

Campese S, 2015, Arxiv, DOI arXiv:1511.00547

[9] Multivariate Gaussian approximations on Markov chaoses [J].

Campese, Simon ;

Nourdin, Ivan ;

Peccati, Giovanni ;

Poly, Guillaume .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2016, 21

[10] Optimal Rate of Convergence for Vector-valued Wiener-Ito Integral [J].

Chen, Huiping .

ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2024, 21 :179-214

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