Non-uniform Berry–Esseen bounds via Malliavin–Stein method

Nguyen Tien Dung; Le Vi; Pham Thi Phuong Thuy

doi:10.5802/crmath.688

Article de recherche - Probabilités

Non-uniform Berry–Esseen bounds via Malliavin–Stein method
[Limites de Berry–Esseen non uniformes par la méthode de Malliavin–Stein]

Nguyen Tien Dung ¹ ; Le Vi ¹ ; Pham Thi Phuong Thuy ²

¹ Department of Mathematics, VNU University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, 084 Vietnam
² The faculty of Basic Sciences, Vietnam Air Defence and Air Force Academy, Son Tay, Hanoi, 084 Vietnam

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 455-463.

Abstract (VO)
Résumé

In this paper, we establish non-uniform Berry–Esseen bounds by means of the Malliavin–Stein method. Applications to the multiple Wiener–Itô integrals and the exponential functionals of Brownian motion are given to illustrate the theory.

Dans cet article, nous établissons des bornes de Berry–Esseen non uniformes au moyen de la méthode de Malliavin–Stein. Des applications aux intégrales multiples de Wiener–Itô et aux fonctions exponentielles du mouvement brownien sont données pour illustrer la théorie.

Reçu le : 2024-09-03
Accepté le : 2024-09-13
Publié le : 2025-05-26

DOI : 10.5802/crmath.688

Classification : 60F05, 60G15, 60H07
Keywords: Malliavin–Stein method, non-uniform Berry–Esseen bound
Mots-clés : Méthode de Malliavin–Stein, limite de Berry–Esseen non uniforme

Affiliations des auteurs :

Nguyen Tien Dung ¹ ; Le Vi ¹ ; Pham Thi Phuong Thuy ²

¹ Department of Mathematics, VNU University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, 084 Vietnam
² The faculty of Basic Sciences, Vietnam Air Defence and Air Force Academy, Son Tay, Hanoi, 084 Vietnam

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Nguyen Tien Dung and Le Vi and Pham Thi Phuong Thuy},
     title = {Non-uniform {Berry{\textendash}Esseen} bounds via {Malliavin{\textendash}Stein} method},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {455--463},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     year = {2025},
     doi = {10.5802/crmath.688},
     language = {en},
}

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Nguyen Tien Dung; Le Vi; Pham Thi Phuong Thuy. Non-uniform Berry–Esseen bounds via Malliavin–Stein method. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 455-463. doi : 10.5802/crmath.688. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.688/

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