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On the functional central limit theorem for martingales. (English) Zbl 0336.60047


MSC:

60B10 Convergence of probability measures
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[1] Billingsley, P., The Lindeberg-Lévy theorem for martingales, Proc. Amer. Math. Soc., 12, 788, 792 (1961) · Zbl 0129.10701
[2] Billingsley, P., Convergence of Probability Measures (1968), New York: Wiley, New York · Zbl 0172.21201
[3] Brown, B. M., Martingale central limit theorems, Ann. Math. Statist., 42, 59-66 (1971) · Zbl 0218.60048
[4] Burkholder, D. L., Distribution function inequalities for martingales, Ann. Probability, 1, 19 42 (1973) · Zbl 0301.60035
[5] Chung, K. L., A Course in Probability Theory (1968), New York: Harcourt, Brace & World, New York · Zbl 0159.45701
[6] Drogin, R., An invariance principle for martingales, Ann. Math. Statist., 2, 602-620 (1972) · Zbl 0243.60029
[7] Dvoretsky, A., Central limit theorems for dependent random variables (1972), Berkeley: Univ. of Calif. Press, Berkeley
[8] Ibragimov, I. A., A central limit theorem for a class of dependent random variables, Theor. Prob. Appl., 7, 83-89 (1962) · Zbl 0123.36103
[9] Levy, P., Theorie de l’addition des Variables Aléatories (1954), Paris: Gauthier-Villars, Paris · Zbl 0056.35903
[10] McLeish, D. L., Dependent central limit theorems and invariance principles, Ann. Probability, 2, 620-628 (1974) · Zbl 0287.60025
[11] Scott, D. J., Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach, Adv. in Appl. Probability, 5, 119-137 (1973) · Zbl 0263.60011
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