Exact rates of convergence in some martingale central limit theorems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:469

Article

Fan, Xiequan^1,2 

[1] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

[2] INRIA, Regular Team, Rocquencourt, France

关键词: Martingales;    Central limit theorem;    Berry-Esseen bounds;   

DOI  :  10.1016/j.jmaa.2018.09.049

来源: Elsevier

【 摘 要 】

Renz [14], Ouchti [13], El Machkouri and Ouchti [3] and Mourrat [12] have established some tight bounds on the rate of convergence in the central limit theorem for martingales. In the present paper a modification of the methods, developed by Bolthausen [1] and Grama and Haeusler [7], is applied for obtaining exact rates of convergence in the central limit theorem for martingales with differences having conditional moments of order 2 + rho, rho > 0. Our results generalise and strengthen the bounds mentioned above. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free