IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v127y2017i8p2725-2750.html
   My bibliography  Save this article

Study of almost everywhere convergence of series by mean of martingale methods

Author

Listed:
  • Cuny, Christophe
  • Fan, Ai Hua

Abstract

Martingale methods are used to study the almost everywhere convergence of general function series. Applications are given to ergodic series, which improves recent results of Fan (2015), and to dilated series, including Davenport series, which completes results of Gapošhkin (1967) (see also Gapošhkin (1968)). Applications are also given to the almost everywhere convergence with respect to Riesz products of lacunary series.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:8:p:2725-2750
    DOI: 10.1016/j.spa.2016.12.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414916302393
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2016.12.006?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. 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.
    2. Hannan, E. J., 1979. "The central limit theorem for time series regression," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 281-289, December.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 710-738, June.
    4. Morten Ørregaard Nielsen, 2005. "Semiparametric Estimation in Time‐Series Regression with Long‐Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 279-304, March.
    5. 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.
    6. James A. Duffy, 2015. "Uniform Convergence Rates over Maximal Domains in Structural Nonparametric Cointegrating Regression," Economics Papers 2015-W03, Economics Group, Nuffield College, University of Oxford.
    7. Morten Ø. Nielsen & Per Houmann Frederiksen, 2008. "Fully Modified Narrow-band Least Squares Estimation Of Stationary Fractional Cointegration," Working Paper 1171, Economics Department, Queen's University.
    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. 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.
    11. Sayar Karmakar & Marek Chudy & Wei Biao Wu, 2020. "Long-term prediction intervals with many covariates," Papers 2012.08223, arXiv.org, revised Sep 2021.
    12. Ronald Kwon & Brigitte Flores & Haydee Yonamine, 2018. "Spatial Segregation and the Impact of Linguistic Multicultural Policies Within the USA," Journal of International Migration and Integration, Springer, vol. 19(2), pages 213-232, May.
    13. Robinson, Peter M., 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
    14. Barry G. Quinn, 2021. "Fisher's g Revisited," International Statistical Review, International Statistical Institute, vol. 89(2), pages 402-419, August.
    15. Peligrad, Magda, 2020. "A new CLT for additive functionals of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5695-5708.
    16. 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.
    17. Wang, Qiying & Lin, Yan-Xia & Gulati, Chandra M., 2001. "Asymptotics for moving average processes with dependent innovations," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 347-356, October.
    18. Liudas Giraitis & Peter M Robinson, 2001. "Parametric Estimation under Long-Range Dependence," STICERD - Econometrics Paper Series 416, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    19. Mynbayev, Kairat & Darkenbayeva, Gulsim, 2019. "Analyzing variance in central limit theorems," MPRA Paper 101685, University Library of Munich, Germany.
    20. Giraitis, Liudas & Robinson, Peter M., 2001. "Parametric estimation under long-range dependence," LSE Research Online Documents on Economics 2227, London School of Economics and Political Science, LSE Library.

    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:127:y:2017:i:8:p:2725-2750. 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/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.