Skip to main content

Approximation of stationary processes and the central limit problem

  • Conference paper
  • First Online:
Probability Theory and Mathematical Statistics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1299))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
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. D. J. Aldous and G. K. Eagleson: On mixing and stability of limit theorems, Ann. Probab. 6 (1978), 325–331.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Billingsley: Convergence of Probability Measures, Wiley, New York (1968).

    MATH  Google Scholar 

  4. G. K. Eagleson: On Gordin's central limit theorem for stationary processes, J. Appl. Probab. 12 (1975), 176–179.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. I. Gordin: The central limit theorem for stationary processes, Soviet Math. Doklady 10 (1969), 1174–1176.

    MathSciNet  MATH  Google Scholar 

  6. P. Hall and C. C. Heyde: Martingale Limit Theory and Its Application, Academic Press, New York (1980).

    MATH  Google Scholar 

  7. D. L. McLeish: Dependent central limit theorems and invariance principles, Ann. Probab. 2 (1974), 620–628.

    Article  MathSciNet  MATH  Google Scholar 

  8. T. Mori and K. Yoshihara: A note on the central limit theorem for stationary strong mixing sequences, to appear in Yokohama Math. J.

    Google Scholar 

  9. W. Parry: Topics in Ergodic Theory, Cambridge Univ. Press, Cambridge (1980).

    MATH  Google Scholar 

  10. P. Shields: The Theory of Bernoulli Shifts, The Univ. Chicago Press, Chicago (1973).

    MATH  Google Scholar 

  11. D. Volný: A negative answer to the central limit problem for strictly stationary processes, Proceedings 3rd Prague Symp. Asymptot. Statistics, Elsevier Sci. Publ., Amsterdam (1984).

    Google Scholar 

  12. D. Volný: The central limit problem for strictly stationary sequences (in Czech): Ph.D. thesis, Math. Institute Charles Univ. Prague, Prague (1984).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Shinzo Watanabe Jurii Vasilievich Prokhorov

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Volný, D. (1988). Approximation of stationary processes and the central limit problem. In: Watanabe, S., Prokhorov, J.V. (eds) Probability Theory and Mathematical Statistics. Lecture Notes in Mathematics, vol 1299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078512

Download citation

  • DOI: https://doi.org/10.1007/BFb0078512

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18814-8

  • Online ISBN: 978-3-540-48187-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics