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Departure from independence: The strong law, standard and random-sum central limit theorems

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References

  1. F. J. Anscombe, Large-sample theory of sequential estimation,Proc. Cambridge Philos. Soc.,48 (1952), pp. 600–607.

    Google Scholar 

  2. J. R. Blum, D. L. Hanson, andJ. I. Rosenblatt, On the central limit theorem for the sum of a random number of independent random variables,Z. Wahrscheinlichkeitstheorie und Verw. Gebiete,1 (1963), pp. 389–393.

    Google Scholar 

  3. H. Cramèr,Mathematical methods of statistics (Princeton, 1956).

  4. M. Csörgő, On the strong law of large numbers and the central limit theorem for martingales, submitted for publication toTrans. Am. Math. Soc.,131 (1968), pp. 259–275.

    Google Scholar 

  5. J. L. Doob,Stochastic processes (Wiley, 1953).

  6. W. Feller,An introduction to probability theory and its applications, Vol. II (Wiley, 1966).

  7. M. Kac, On the distribution of values of sums of the type Σf(2k t)Ann. of Math.,47 (1946), pp. 33–49.

    Google Scholar 

  8. P. Lévy, Propriétés asymptotiques des sommes de variables aleatoires independantes ou enchainees,J. Math. Pures Appl. Ser8 14 (1935), pp. 347–402.

    Google Scholar 

  9. M. Loève,Probability theory (Van Nostrand, 1960).

  10. J. Mogyoródi, A central limit theorem for the sum of a random number of independent random variables,Publications of the Math. Inst. of the Hung. Acad. of Sci.,7A (1962), pp. 409–424.

    Google Scholar 

  11. A. Rényi, On the asymptotic distribution of the sum of a random number of independent random variables,Acta Math. Acad. Sci. Hung.,8 (1957), pp. 193–197.

    Google Scholar 

  12. A. Rényi, On mixing sequences of sets,Acta Math. Acad. Sci. Hung.,9 (1958), pp. 215–228.

    Google Scholar 

  13. A. Rényi, On the central limit theorem for the sum of a random number of independent random variables,Acta Math. Acad. Sci. Hung.,11 (1960), pp. 97–102.

    Google Scholar 

  14. S. Takahashi, On the central limit theorem,Tohoku Math. J.,3 (1951), pp. 316–321.

    Google Scholar 

  15. H. Wittenberg, Limiting distributions of random sums of independent random variables,Z. Wahrscheinlichkeitstheorie und Verw. Gebiete,3 (1964), pp. 7–18.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, McGill University, Montreal, Canada

    M. Csörgő

  2. Department of Mathematics, Carleton University, Ottawa, Canada

    R. Fischler

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  1. M. Csörgő
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  2. R. Fischler
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In memory of ProfessorAlfréd Rényi

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Csörgő, M., Fischler, R. Departure from independence: The strong law, standard and random-sum central limit theorems. Acta Mathematica Academiae Scientiarum Hungaricae 21, 105–114 (1970). https://doi.org/10.1007/BF02022494

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