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The generalized anscombe condition and its applications in random limit theorems

  • E. Rychlik
  • Z. Rychlik
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 828)

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References

  1. [1]
    Aldous, D.J. Weak convergence of randomly indexed sequences of random variables. Math.Proc.Camb.Phil.Soc. 83(1978), 117–126MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Aldous, D.J. and Eagleson, G.K. On mixing and stability of limit theorems. Ann.Probability 6(1978), 325–331.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Anscombe, F.J. Large-sample theory of sequential estimation. Proc.Cambridge Philos.Soc. 48 (1952), 600–607.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Babu, G.J. and Ghosh, M. A random functional central limit theorems for margingales. Acta Math.Acad.Sci.Hung. 27(1976), 301–306.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Bhattacharya, R.N. and Ranga Rao R. Normal Approximation and Asymptotic Expansions. John Wiley 1976.Google Scholar
  6. [6]
    Billingsley, P. Convergence of probability measures. New York: Wiley 1968.zbMATHGoogle Scholar
  7. [7]
    Blum, J.R., Hanson, D.I. and Rosenblatt, J.I. On the central limit theorem for the sum of a random number of independent random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 1(1963), 389–393.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Byczkowski, T. and Inglot, T. The invariance principle for vector-valued random variables with applications to functional random limit theorems. (to appear)Google Scholar
  9. [9]
    Csörgö, M. and Rychlik, Z. Weak convergence of sequences of random elements with random indices. Math.Proc.Camb.Phil. Soc.(submitted)Google Scholar
  10. [10]
    Csörgö, M. and Rychlik, Z. Asymptotic properties of randomly indexed sequences of random variables. Carleton Mathematical Lecture Note No. 23, July 1979.Google Scholar
  11. [11]
    Guiasu, S. On the asymptotic distribution of sequences of random variables with random indices. Ann.Math.Statist.42 (1971), 2018–2028.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Prakasa Rao, B.L.S. Limit theorems for random number of random elements on complete separable metric spaces. Acta Math.Acad.Sci. Hung. 24(1973), 1–4.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • E. Rychlik
    • 1
    • 2
  • Z. Rychlik
    • 1
    • 2
  1. 1.Instytut MatematykiUniwersytet WarszawskiWarszawaPoland
  2. 2.Instytut Matematyki UMCSLublinPoland

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