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

Abstract

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.

References in corpus (2)

• Cramér Type Moderate Deviations for Random Fields
• A Local Limit Theorem for Linear Random Fields