Skip to main content
SpringerLink
Log in

Some limit theorems for summability methods of I.I.D.Random variables

  • Conference paper
  • First Online:
Stability Problems for Stochastic Models

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1233))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bingham, N.H.: On Borel and Euler summability. J.London, Math.Soc.29,(1984) 141–146.

    Article  MathSciNet  MATH  Google Scholar 

  2. Dingham, N.H. and Maejima, M.: Summability methods and almost sure convergence Z.Wahrscheinlichkeitstheorie verw. Gebiete 68, (1985), 383–392.

    Article  MathSciNet  MATH  Google Scholar 

  3. Bingham, N.H. and Tenenbaum, G.(1985): Riesz and Valiron means and fractional moments. To appear.

    Google Scholar 

  4. Chow, Y.S.: Delayed sums and Borel summability of independent, identically distributed random variables. Bull. Inst. Math.Acad. Sinica 1 (1973), 207–220.

    MathSciNet  MATH  Google Scholar 

  5. Embrechts, P. and Maejima, M.: The central limit theorem for summability methods of i.i.d. random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 68 (1984), 191–204.

    Article  MathSciNet  MATH  Google Scholar 

  6. Greber, H.U.: The discounted central limit theorem and its Berry-Esséen analogue.Ann. Math. Statist. 42 (1971), 389–392.

    Article  MathSciNet  MATH  Google Scholar 

  7. Jöckel, K.H. and Sendler, W.: A central limit theorem for generalized disccounting. Math. Operationsforsh.Statist., Ser.Statist.12, (1981), 605–608.

    Article  Google Scholar 

  8. Karamata, J.: Sur la rapport entre les convergences d'une suite de fonctions et de leurs moments, avec application à l'inversion des procédés de sommabilité. Studia Math. 3 (1931), 68–76.

    MATH  Google Scholar 

  9. Kasahara,Y. and Maejima, M.(1985):Functional limit theorems for weighted sums of i.i.d. random variables. Preprint.

    Google Scholar 

  10. Lai, T.L.: Summability methods for independent, identically distributed random variables. Proc.Amer.Math.Soc. 45 (1974), 253–261

    MathSciNet  MATH  Google Scholar 

  11. Maejima,M. and Rachev, S.T.: An ideal metric and the rate of convergence to a self-similar process. Preprint.

    Google Scholar 

  12. Omey, E.: A limit theorem for discounted sums. Z. Wahrscheinlichkeitstheorie verw. Gebiete 68 (1984), 49–51.

    Article  MathSciNet  MATH  Google Scholar 

  13. Shukri, E.M.: Local limit theorems for sums of weighted independent random variables. Theory Probab. Appl. 21 (1976), 137–144.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Keio University, Yokohama, Japan

    Makoto Maejima

Authors
  1. Makoto Maejima
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Vladimir V. Kalashnikov Boyan Penkov Vladimir M. Zolotarev

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Maejima, M. (1987). Some limit theorems for summability methods of I.I.D.Random variables. In: Kalashnikov, V.V., Penkov, B., Zolotarev, V.M. (eds) Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol 1233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072711

Download citation

  • DOI: https://doi.org/10.1007/BFb0072711

  • Received:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17204-8

  • Online ISBN: 978-3-540-47394-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation