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  • Wu, Songqi; Ma, Xiaohui; Sang, Hailin; Fan, Xiequan

    arXiv.org, 02/2020
    Paper

    Renz (Ann. Probab. 1996) has established a rate of convergence \(1/\sqrt{n}\) in the central limit theorem for martingales with some restrictive conditions. In the present paper a modification of the methods, developed by Bolthausen (Ann. Probab. 1982) and Grama and Haeusler (Stochastic Process. Appl. 2000), is applied for obtaining the same convergence rate for a class of more general martingales. An application to linear processes is discussed.