English

A Berry-Esseen bound of order $ 1/\sqrt{n} $ for martingales

Probability 2020-02-04 v1

Abstract

Renz (Ann. Probab. 1996) has established a rate of convergence 1/n1/\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.

Keywords

Cite

@article{arxiv.2002.00307,
  title  = {A Berry-Esseen bound of order $ 1/\sqrt{n} $ for martingales},
  author = {Songqi Wu and Xiaohui Ma and Hailin Sang and Xiequan Fan},
  journal= {arXiv preprint arXiv:2002.00307},
  year   = {2020}
}