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Weak convergence to stable laws by means of a weak invariance principle

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Book cover Empirical Distributions and Processes

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 566))

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The work of this author was supported by the United States Air Force Office of Scientific Research under Grant No. AFOSR-75-2796.

The work of this author was supported by the United States National Science Foundation.

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References

  1. Csörgö, M. and Révész, P. (1975). A new method to prove Strassen type laws of invariance principle. I. Z. Wahrscheinlichkeitstheorie Verv. Gebiete 31, 255–259.

    Article  MATH  Google Scholar 

  2. Doeblin, W. (1940). Sur l' ensemble de pruissances d' une loi de probabilité. Studia Math. 9, 71–96.

    MathSciNet  MATH  Google Scholar 

  3. Gnedenko, B. V. (1940) (in Russian). Some theorems on the powers of distribution functions. Uchenye Zapiski Moskov. Gos. Univ. Mathematika 45, 61–72.

    MathSciNet  Google Scholar 

  4. Komlós, J., Major, P. and Tusnády, G. (1975). An approximation of partial sums of independent RV's and DF. I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 32, 111–131.

    Article  MathSciNet  MATH  Google Scholar 

  5. Lévy, Paul (1954). Théorie de l' Addition des Variables Aléatories, 2nd ed. Paris: Guathier-Villars.

    Google Scholar 

  6. Loève, M. (1963). Probability Theory, 3rd ed. Princeton, New Jersey: Van Nostrand.

    MATH  Google Scholar 

  7. Philipp, W., and Stout, W. (1975). Almost sure invariance principles for partial sums of weakly dependent random variables. Amer. Math. Soc. Mem. No. 161. Amer. Math. Soc., Providence, Rhode Island.

    MATH  Google Scholar 

  8. Root, D. and Rubin, H. (1973). A probabilistic proof of the normal convergence criterion. Ann. Prob. 1, 867–869.

    Article  MathSciNet  MATH  Google Scholar 

  9. Strassen, V. (1964). An invariance principle for the law of the iterated logarithm. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3, 211–226.

    Article  MathSciNet  MATH  Google Scholar 

  10. Strassen, V. (1965). Almost sure behavior of sums of independent random variables and martingales. Proc. Fifth Berkeley Symp. Math. Statist. Prob. 2, 315–343.

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 61801, Urbana, Illinois

    Gordon Simons & William Stout

Authors
  1. Gordon Simons
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  2. William Stout
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Peter Gaenssler Pál Révész

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© 1976 Springer-Verlag

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Simons, G., Stout, W. (1976). Weak convergence to stable laws by means of a weak invariance principle. In: Gaenssler, P., Révész, P. (eds) Empirical Distributions and Processes. Lecture Notes in Mathematics, vol 566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096883

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  • DOI: https://doi.org/10.1007/BFb0096883

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08061-9

  • Online ISBN: 978-3-540-37515-9

  • eBook Packages: Springer Book Archive

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