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On a problem of necessary and sufficient conditions in the functional central limit theorem for local martingales. (English) Zbl 0482.60030

MSC:
60F17 Functional limit theorems; invariance principles
60G48 Generalizations of martingales
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[4] Jacod, J.: Calcul stochastique et problémes de martingales. Lecture Notes in Math. 714. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0414.60053
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[9] McLeish, D.L.: An extended martingale principle. Ann Probab. 6, 144-150 (1978) · Zbl 0379.60046 · doi:10.1214/aop/1176995619
[10] Rebolledo, R.: Sur le théoréme de a limite central pour les martingales. C.R. Acad. Sci. Paris Sér., A288, 879-882 (1979) · Zbl 0396.60047
[11] Rebolledo, R.: The central limit theorem for semimartingales: necessary and sufficient conditions. Z. Wahrscheinlichkeitstheorie verw. Gebiete (1981); preprint
[12] Rootzen, H.: On the functional central limit theorem for martingales, I, II. Z. Wahrscheinlichkeitstheorie verw. Gebiete 38, 199-210 (1977); 51, 77-93 (1980) · Zbl 0336.60047 · doi:10.1007/BF00537263
[13] Stone, C.: Weak convergence of stochastic processes defined on semi-finite time intervals. Proc. Amer. Math. Soc. 694-696 (1963) · Zbl 0116.35602
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