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References
Billingsley, P.: Convergence of probability measures. New York: Wiley 1968
Blake, L.: A generalization of martingale and two consequent convergence theorems. Pacific J. Math.35, 2, 279–284 (1970)
Doob, I.L.: Stochastic processes. New York: Wiley 1953
Gordin, I.M.: The central limit theorem for stationary processes. Soviet. Math. Dokl.10, 1174–1176 (1969)
Iosifescu, M., Theodorescu, R.: Random processes and learning. Berlin Heidelberg New York: Springer 1969
Meyer, P.A.: Probabilités et potentiel. Paris: Hermann 1966
Mucci, A.G.: Another martingale convergence theorem. Pacific J. Math.,64, 2, 539–542 (1976)
McLeish, D.L.: Invariance principles for dependent variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete32, 165–178 (1975)
McLeish, D.L.: On the invariance principle for nonstationary mixingales, Ann. Probability,5, 616–621 (1977)
Peligrad, M.: Limit theorems and law of the large numbers for martingale-like sequences. Math. Nachr.99, (1981) [To appear ]
Philipp, W., Webb, G.R.: An invariance principle for mixing sequences of random variables. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete,25, 223–237 (1973)
Renyi, A.: On mixing sequences of random variables. Acta Math. Acad. Sci. Hungar.9, 389–393 (1958)
Serfling, R.J.: Contributions to central limit theory for dependent variables. Ann. Math. Statist.39, 1158–1175 (1968)
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Peligrad, M. An invariance principle for dependent random variables. Z. Wahrscheinlichkeitstheorie verw Gebiete 57, 495–507 (1981). https://doi.org/10.1007/BF01025871
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DOI: https://doi.org/10.1007/BF01025871