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Remarks on the functional central limit theorem for martingales. (English) Zbl 0402.60032


MSC:

60F17 Functional limit theorems; invariance principles

Citations:

Zbl 0336.60047
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References:

[1] Aldous, D., Stopping times and tightness, Ann. Probability, 6, 335-340 (1978) · Zbl 0391.60007
[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] Gänssler, P.; Stute, W., Wahrscheinlichkeitstheorie. Springer Hochschultext (1977), Berlin-Heidelberg-NewYork: Springer, Berlin-Heidelberg-NewYork · Zbl 0357.60001
[5] McLeish, D. L., Dependent central limit theorems and invariance principles, Ann. Probability, 2, 620-628 (1974) · Zbl 0287.60025
[6] Rootzén, H., On the functional central limit theorem for martingales, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 38, 199-210 (1977) · Zbl 0336.60047
[7] Rootzén, H.: On the functional central limit theorem for martingales, part II. Z. Wahrscheinlichkeitstheorie verw. Gebiete 51 (1980) · Zbl 0402.60033
[8] Scott, D. J., Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach, Advances in Appl. Probability, 5, 119-137 (1973) · Zbl 0263.60011
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