IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v85y2014icp161-167.html
   My bibliography  Save this article

Quenched central limit theorems for sums of stationary processes

Author

Listed:
  • Volný, Dalibor
  • Woodroofe, Michael

Abstract

It is shown that the existence of an L1 martingale–coboundary decomposition does not imply the quenched version of the Central Limit Theorem. In another result, it is shown that a condition proposed by Hannan does imply quenched convergence for a centered version of the sum while a condition proposed by Heyde does not imply quenched convergence.

Suggested Citation

  • Volný, Dalibor & Woodroofe, Michael, 2014. "Quenched central limit theorems for sums of stationary processes," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 161-167.
    • Handle: RePEc:eee:stapro:v:85:y:2014:i:c:p:161-167
    DOI: 10.1016/j.spl.2013.09.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715213003313
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2013.09.033?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Woodroofe, Michael, 1992. "A central limit theorem for functions of a Markov chain with applications to shifts," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 33-44, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Magda Peligrad & Dalibor Volný, 2020. "Quenched Invariance Principles for Orthomartingale-Like Sequences," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1238-1265, September.
    2. Na Zhang & Lucas Reding & Magda Peligrad, 2020. "On the Quenched Central Limit Theorem for Stationary Random Fields Under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2351-2379, December.
    3. Barrera, David & Peligrad, Costel & Peligrad, Magda, 2016. "On the functional CLT for stationary Markov chains started at a point," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 1885-1900.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alsmeyer, Gerold & Buckmann, Fabian, 2019. "An arcsine law for Markov random walks," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 223-239.
    2. Biao Wu, Wei & Min, Wanli, 2005. "On linear processes with dependent innovations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 939-958, June.
    3. 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.
    4. Klicnarová, Jana & Volný, Dalibor, 2009. "On the exactness of the Wu-Woodroofe approximation," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2158-2165, July.
    5. L. Ouchti & D. Volný, 2008. "A Conditional CLT which Fails for Ergodic Components," Journal of Theoretical Probability, Springer, vol. 21(3), pages 687-703, September.
    6. Gerold Alsmeyer & Chiranjib Mukherjee, 2023. "On Null-Homology and Stationary Sequences," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-25, March.
    7. Holzmann, Hajo, 2005. "Martingale approximations for continuous-time and discrete-time stationary Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1518-1529, 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:stapro:v:85:y:2014:i:c:p:161-167. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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/622892/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.