IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v44y1993i1p41-74.html
   My bibliography  Save this article

Approximating martingales and the central limit theorem for strictly stationary processes

Author

Listed:
  • Volný, Dalibor

Abstract

The proofs of various central limit theorems for strictly stationary sequences of random variables are based on approximating the partial sums of the process by martingales (cf., e.g., Gordin, 1969; Dürr and Goldstein, 1984; or Hall and Heyde, 1980, Chapter 5). Here we shall give a study on the assumptions of such theorems and introduce new ones. Then we shall discuss conditions under which the results take place in almost all ergodic components simultaneously and present an application to the limit theory of stationary linear proceses with random coefficients.

Suggested Citation

  • Volný, Dalibor, 1993. "Approximating martingales and the central limit theorem for strictly stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 41-74, January.
    • Handle: RePEc:eee:spapps:v:44:y:1993:i:1:p:41-74
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(93)90037-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yokoyama, Ryozo, 1995. "On the central limit theorem and law of the iterated logarithm for stationary processes with applications to linear processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 343-351, October.
    2. Cuny, Christophe & Fan, Ai Hua, 2017. "Study of almost everywhere convergence of series by mean of martingale methods," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2725-2750.
    3. Peligrad, Magda, 2020. "A new CLT for additive functionals of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5695-5708.
    4. Dedecker, Jérôme & Merlevède, Florence, 2011. "Rates of convergence in the central limit theorem for linear statistics of martingale differences," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1013-1043, May.
    5. Jérôme Dedecker & Florence Merlevède & Dalibor Volný, 2007. "On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 20(4), pages 971-1004, December.
    6. Lesigne, Emmanuel & Volný, Dalibor, 2001. "Large deviations for martingales," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 143-159, November.
    7. Dede, Sophie, 2009. "An empirical Central Limit Theorem in for stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3494-3515, October.
    8. Magda Peligrad & Hailin Sang, 2013. "Central Limit Theorem for Linear Processes with Infinite Variance," Journal of Theoretical Probability, Springer, vol. 26(1), pages 222-239, March.
    9. Wu, Wei Biao, 2009. "An asymptotic theory for sample covariances of Bernoulli shifts," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 453-467, February.
    10. Volný, Dalibor & Wang, Yizao, 2014. "An invariance principle for stationary random fields under Hannan’s condition," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4012-4029.
    11. Dalibor Volný, 2010. "Martingale Approximation and Optimality of Some Conditions for the Central Limit Theorem," Journal of Theoretical Probability, Springer, vol. 23(3), pages 888-903, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:44:y:1993:i:1:p:41-74. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.