L 1 bounds for some martingale central limit theorems

Abstract

The aim of this paper is to extend the results in [E. Bolthausen, Exact convergence rates in some martingale central limit theorems, Ann. Probab., 10(3):672–688, 1982] and [J.C. Mourrat, On the rate of convergence in the martingale central limit theorem, Bernoulli, 19(2):633–645, 2013] to the L1-distance between distributions of normalized partial sums for martingale-difference sequences and the standard normal distribution.