@article{AIHPB_2005__41_1_35_0, author = {Ouchti, Lahcen}, title = {On the rate of convergence in the central limit theorem for martingale difference sequences}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, volume = {41}, year = {2005}, pages = {35-43}, doi = {10.1016/j.anihpb.2004.03.003}, mrnumber = {2110445}, zbl = {1063.60060}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPB_2005__41_1_35_0} }
Ouchti, Lahcen. On the rate of convergence in the central limit theorem for martingale difference sequences. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) pp. 35-43. doi : 10.1016/j.anihpb.2004.03.003. http://gdmltest.u-ga.fr/item/AIHPB_2005__41_1_35_0/
[1] The accuracy of the Gaussian approximation to the sum of independent variates, Trans. Amer. Math. Soc. 49 (1941) 122-136. | JFM 67.0461.01 | MR 3498
,[2] Convergence of Probability Measures, Wiley, 1968. | MR 233396 | Zbl 0172.21201
,[3] Exact convergence rates in some martingale central limit theorems, Ann. Probab. 10 (3) (1982) 672-688. | MR 659537 | Zbl 0494.60020
,[4] M. El Machkouri, D. Volný, On the central and local limit theorems for martingale difference sequences, Stochastics and Dynamics, submitted for publication. | MR 2069687 | Zbl 1080.60015
[5] On the Liapounoff limit of error in the theory of probability, Ark. Math. Astr. och Fysik A 28 (1942) 1-19. | JFM 68.0277.02 | MR 11909
,[6] Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading, MA, 1954, translated by K.L. Chung. | MR 62975 | Zbl 0056.36001
, ,[7] W.F. Grams, Rate of convergence in the central limit theorem for dependent variables, Dissertation, Florida State Univ., 1972.
[8] On the rate of convergence in the central limit theorem for martingales with discrete and continuous time, Ann. Probab. 16 (1) (1988) 275-299. | MR 920271 | Zbl 0639.60030
,[9] On the rate of convergence in mean central limit theorem for martingale differences, Rep. Statist. Appl. Res. Un. Japan. Sci. Engrs. 23 (1976) 10-15. | MR 451362 | Zbl 0372.60063
,[10] Martingale Limit Theory and Its Application, Academic Press, New York, 1980. | MR 624435 | Zbl 0462.60045
, ,[11] A central limit theorem for a class of dependent random variables, Theory Probab. Appl. 8 (1963) 83-89. | MR 151997 | Zbl 0123.36103
,[12] Rates of convergence in central limit theorem for martingale differences, Bull. Math. Statist. 18 (1979) 1-8. | MR 517156 | Zbl 0401.60018
,[13] Probability Theory, D. Van Nostrand, Princeton, NJ, 1955. | MR 123342 | Zbl 0108.14202
,