On the rate of convergence in some mean martingale central limit theorems

Abstract

Let (Xk,1≤k≤n) be a sequence of martingale differences with respect to σ-fields Ƒₒ⊂ Ƒ₁⊂...⊂Ƒn, where the variance of Xk may be tinite or intinite. The aim of this article is to establish the rate of convergence in the mean Central limit theorems for the sum Sn -X₁ +...+Xn by uniting the method of Bolthausen [2], Haeusler [8] and the result of Röllin [10].