Exact rates of convergence in some martingale central limit theorems

Renz 14], Ouchti 13], El Machkouri and Ouchti 3] and Mourrat 12] have established some tight bounds on the rate of convergence in the central limit theorem for martingales. In the present paper a modification of the methods, developed by Bolthausen 1] and Grama and Haeusler 7], is applied for obtaining exact rates of convergence in the central limit theorem for martingales with differences having conditional moments of order $2+\rho ,\rho >0$. Our results generalise and strengthen the bounds mentioned above.