Skip to main content
SpringerLink
Log in

Martingale approximation of non adapted stochastic processes with nonlinear growth of variance

  • Chapter
Dependence in Probability and Statistics

Part of the book series: Lecture Notes in Statistics ((LNS,volume 187))

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Jérôme Dedecker and Florence Merlevède. Necessary and sufficient conditions for the conditional central limit theorem. Annals of Probabability, 30(3):1044–1081, 2002.

    MATH  Google Scholar 

  2. Yves Derriennic and Michael Lin. Fractional Poisson equations and ergodic theorems for fractional coboundaries. Israel Journal of Mathematics, 123:93–130, 2001.

    MATH  MathSciNet  Google Scholar 

  3. Peter Gänssler and Erich Häusler. Remarks on the functional central limit theorem for martingales. Zeitschrift für Wahrscheinligkeits Theorie und Verwandte Gebiete, 50(3):237–243, 1979.

    Article  MATH  Google Scholar 

  4. M. I. Gordin. The central limit theorem for stationary processes. Doklady Akademii Nauk SSSR, 188:739–741, 1969.

    MATH  MathSciNet  Google Scholar 

  5. Peter Hall and Chris C. Heyde. Martingale limit theory and its application. Academic Press, Harcourt Brace Jovanovich Publishers, New York, 1980. Probability and Mathematical Statistics.

    MATH  Google Scholar 

  6. Idlar A. Ibragimov and Yu. V. Linnik. Independent and stationary sequences of random variables. Wolters-Noordhoff Publishing, Groningen, 1971. With a supplementary chapter by I. A. Ibragimov and V. V. Petrov, Translation from the Russian edited by J. F. C. Kingman.

    MATH  Google Scholar 

  7. J. Klicnarová and Dalibor Volný. On optimal martingale approximation. Preprint, 2005.

    Google Scholar 

  8. Michael Maxwell and Michael Woodroofe. Central limit theorems for additive functionals of Markov chains. Annals of Probability, 28(2):713–724, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  9. L. Ouchti and Dalibor Volný. A conditional CLT which fails in all ergodic components Preprint, 2005.

    Google Scholar 

  10. Magda Peligrad and Sergey Utev. A new maximal inequality and invariance principle for stationary sequences. Annals of Probability, 33(2):798–815, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  11. Sidney I. Resnick. Extreme values, regular variation, and point processes, volume 4 of Applied Probability. A Series of the Applied Probability Trust. Springer-Verlag, New York, 1987.

    Google Scholar 

  12. Ludger Rüschendorf. The Wasserstein distance and approximation theorems. Zeitschrift für Wahrscheinligkeits Theorie und Verwandte Gebiete, 70(1):117–129, 1985.

    Article  MATH  Google Scholar 

  13. Dalibor Volný. Martingale decompositions of stationary processes. Yokohama Mathematical Journal, 35(1–2):113–121, 1987.

    MATH  MathSciNet  Google Scholar 

  14. Dalibor Volný. Counter examples to the central limit problem for stationary dependent random variables. Yokohama Mathematical Journal, 36(1):69–78, 1988.

    MathSciNet  Google Scholar 

  15. Dalibor Volný. Approximating martingales and the central limit theorem for strictly stationary processes. Stochastic Processes and Their Applications, 44(1):41–74, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  16. Dalibor Volný. Martingale approximations of stochastic processes depending on the choice of the filtration Preprint, 2005.

    Google Scholar 

  17. Wei Biao Wu. A strong convergence theory for stationary processes. Preprint, 2005.

    Google Scholar 

  18. Wei Biao Wu and Michael Woodroofe. Martingale approximations for sums of stationary processes. Annals of Probability, 32(2):1674–1690, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  19. Ryōzō Yokoyama. On the central limit theorem and law of the iterated logarithm for stationary processes with applications to linear processes. Stochastic Processes and Their Applications, 59(2):343–351, 1995.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, Avenue de l’Université, BP 12, 76801, Saint Etienne du Rouvray

    Dalibor Volný

Authors
  1. Dalibor Volný
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. L-S Timbre J340, CREST, 18 Boulevard Adolphe Pinard, 75675, Paris Cedex 14, France

    Patrice Bertail  & Paul Doukhan  & 

  2. Laboratoire MODAL’X, Université Paris X, 200 avenue de la République, 92000, Nanterre Cedex, France

    Patrice Bertail  & Philippe Soulier  & 

  3. Université de Cergy-Pontoise, 33 boulevard du Port, 95011, Cergy-Pontoise Cedex, France

    Paul Doukhan

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Volný, D. (2006). Martingale approximation of non adapted stochastic processes with nonlinear growth of variance. In: Bertail, P., Soulier, P., Doukhan, P. (eds) Dependence in Probability and Statistics. Lecture Notes in Statistics, vol 187. Springer, New York, NY . https://doi.org/10.1007/0-387-36062-X_7

Download citation

Publish with us

Policies and ethics

Search

Navigation