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The generalized anscombe condition and its applications in random limit theorems

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Probability Theory on Vector Spaces II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 828))

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References

  1. Aldous, D.J. Weak convergence of randomly indexed sequences of random variables. Math.Proc.Camb.Phil.Soc. 83(1978), 117–126

    Article  MathSciNet  MATH  Google Scholar 

  2. Aldous, D.J. and Eagleson, G.K. On mixing and stability of limit theorems. Ann.Probability 6(1978), 325–331.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Babu, G.J. and Ghosh, M. A random functional central limit theorems for margingales. Acta Math.Acad.Sci.Hung. 27(1976), 301–306.

    Article  MathSciNet  MATH  Google Scholar 

  5. Bhattacharya, R.N. and Ranga Rao R. Normal Approximation and Asymptotic Expansions. John Wiley 1976.

    Google Scholar 

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

    MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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. Csörgö, M. and Rychlik, Z. Weak convergence of sequences of random elements with random indices. Math.Proc.Camb.Phil. Soc.(submitted)

    Google Scholar 

  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. Guiasu, S. On the asymptotic distribution of sequences of random variables with random indices. Ann.Math.Statist.42 (1971), 2018–2028.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Instytut Matematyki, Uniwersytet Warszawski, Pałac Kultury i Nauki, 00-901, Warszawa, Poland

    E. Rychlik & Z. Rychlik

  2. Instytut Matematyki UMCS, Nowotki 10, 20-031, Lublin, Poland

    E. Rychlik & Z. Rychlik

Authors
  1. E. Rychlik
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  2. Z. Rychlik
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A. Weron

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© 1980 Springer-Verlag

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Rychlik, E., Rychlik, Z. (1980). The generalized anscombe condition and its applications in random limit theorems. In: Weron, A. (eds) Probability Theory on Vector Spaces II. Lecture Notes in Mathematics, vol 828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097409

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  • DOI: https://doi.org/10.1007/BFb0097409

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10253-3

  • Online ISBN: 978-3-540-38350-5

  • eBook Packages: Springer Book Archive

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