Berry-Ess\'een bound for complex Wiener-It\^{o} integral

Huiping Chen; Yong Chen; Yong Liu

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Berry-Ess\'een bound for complex Wiener-It\^(o) integral

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arxiv 2407.05353 v1 pith:ZV27VYJF submitted 2024-07-07 math.PR

Berry-Ess\'een bound for complex Wiener-It\^(o) integral

Huiping Chen , Yong Chen , Yong Liu This is my paper

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keywords berry-esscomplexboundintegralwiener-itadditionallyapplicationassociated

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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.

Berry-Ess\'een bound for complex Wiener-It\^(o) integral

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