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An invariance principle for mixing sequences of random variables

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References

  1. Billingsley, P.: Convergence of probability measures. New York: Wiley 1968.

    Google Scholar 

  2. Gikhman, I.I., Skorokhod, A.V.: Introduction to the theory of random processes. Philadelphia: Saunders 1969.

    Google Scholar 

  3. Ibragimov, I.A.: Some limit theorems for stationary processes. Theor. Probab. Appl. 7, 349–382 (1962).

    Google Scholar 

  4. Iosifescu, M., Theodorescu, R.: Random processes and learning. Berlin-Heidelberg-New York: Springer 1969.

    Google Scholar 

  5. Loève, M.: Probability theory. 3rd. ed. Princeton: Van Nostrand 1963.

    Google Scholar 

  6. Philipp, W.: The central limit problem for mixing sequences or random variables. Z.Wahrscheinichkeitstheorie verw. Geb. 12, 155–171 (1969).

    Google Scholar 

  7. Philipp, W.: The law of iterated logarithm for mixing stochastic processes. Ann. Math. Statist. 40, 1985–1991 (1969).

    Google Scholar 

  8. Philipp, W.: Mixing sequences of random variables and probabilistic number theory. Memoirs AMS vol. 114, Providence 1971.

  9. Prohorov, Yu.V.: Convergence of random processes and limit theorems in probability theory. Theor. Probab. Appl. 1, 157–214 (1956).

    Google Scholar 

  10. Webb, G.: The functional central limit theorem for nonstationary sequences of mixing random variables. Ph. D. Thesis, Duke University, Durham, N.C., 1970.

    Google Scholar 

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Philipp, W., Webb, G.R. An invariance principle for mixing sequences of random variables. Z. Wahrscheinlichkeitstheorie verw Gebiete 25, 223–237 (1973). https://doi.org/10.1007/BF00535894

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  • DOI: https://doi.org/10.1007/BF00535894

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