Skip to main content

Some central limit theorems for randomly indexed sequences of random vectors

  • 416 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1080)

Keywords

  • Random Vector
  • Central Limit Theorem
  • Weak Convergence
  • Polish Space
  • Dependent Random Variable

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Berkes, I., Philipp, W. Approximation theorems for independent and weakly dependent random variables. Ann.Probab. 7(1979),29–54.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Billingsley, P. Convergence of probabilty measures. New York: J. Wiley (1968).

    MATH  Google Scholar 

  6. Blum, J. R., Hanson, D. I., 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.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Csörgö, M., Rychlik, Z. Weak convergences of sequences of random elements with random indices. Math.Proc.Camb.Phil.Soc. 88(1980) 171–174.

    CrossRef  MATH  Google Scholar 

  8. Mogyoródi, J. A central limit theorem for the sum of a random variables. Publ.Math.Inst.Hung.Acad.Sci. Serie A. 7(1962), 409–424.

    MATH  Google Scholar 

  9. Paulauskas, V. On sums of a random multi-dimensional vectors (in Russian). Lit.Mat.Sb. 12 No 2 (1972), 109–131.

    MathSciNet  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Rychlik, E. Asymptotic distributions of sums of random number of a random multi-dimensional vectors. Lit.Mat.Sb. 22(1982) (2) 150

    MathSciNet  MATH  Google Scholar 

  12. Rychlik, E. Some limitary theorems for randomly indexed sequences of random variables. Bull.Acad.Polon.Sci.,Math.Astronim.Phys. Vol. 31, No. 1–2,(1983), 82–87.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Rychlik, E. (1984). Some central limit theorems for randomly indexed sequences of random vectors. In: Szynal, D., Weron, A. (eds) Probability Theory on Vector Spaces III. Lecture Notes in Mathematics, vol 1080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099800

Download citation

  • DOI: https://doi.org/10.1007/BFb0099800

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13388-9

  • Online ISBN: 978-3-540-38939-2

  • eBook Packages: Springer Book Archive