2023/04/17 by Huiping Chen, Yong Chen, Chen, Huiping +3
Mathematics · #60F05 #60G15 #60H05 #FOS: Mathematics #Mathematical functions and polynomials #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2304.08088
openalex publication_date 2023/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a series of univariate or multivariate complex multiple Wiener-Itô integrals, we appreciably improve the previously known contractions condition of complex Fourth Moment Theorem (FMT) and present a fourth moment type Berry-Esséen bound under Wasserstein distance. Note that in some special cases of univariate complex multiple Wiener-Itô integral, the Berry-Esséen bound we acquired is optimal. A remarkable fact is that the Berry-Esséen bound of multivariate complex multiple Wiener-Itô integral is related to the partially order of the index of the complex multiple Wiener-Itô integral, which has no real counterparts as far as we know. As an application, we explore the asymptotic property for the numerator of a ratio process which originates from the classical Chandler wobble model.