IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v117y2007i8p1137-1164.html
   My bibliography  Save this article

A Hölderian functional central limit theorem for a multi-indexed summation process

Author

Listed:
  • Rackauskas, Alfredas
  • Suquet, Charles
  • Zemlys, Vaidotas

Abstract

Let be an i.i.d. random field of square integrable centered random elements in the separable Hilbert space and , , be the summation processes based on the collection of sets [0,t1]x...x[0,td], 0 =2, we characterize the weak convergence of in the Hölder space by the finiteness of the weak p moment of for p=(1/2-[alpha])-1. This contrasts with the Hölderian FCLT for d=1 and [A. Rackauskas, Ch. Suquet, Necessary and sufficient condition for the Lamperti invariance principle, Theory Probab. Math. Statist. 68 (2003) 115-124] where the necessary and sufficient condition is P(X1>t)=o(t-p).

Suggested Citation

  • Rackauskas, Alfredas & Suquet, Charles & Zemlys, Vaidotas, 2007. "A Hölderian functional central limit theorem for a multi-indexed summation process," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1137-1164, August.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:8:p:1137-1164
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(06)00194-3
    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.

    References listed on IDEAS

    as
    1. Alfredas Račkauskas & Charles Suquet, 2006. "Testing Epidemic Changes of Infinite Dimensional Parameters," Statistical Inference for Stochastic Processes, Springer, vol. 9(2), pages 111-134, July.
    2. Ziegler, Klaus, 1997. "Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 233-272, August.
    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. Daniel Gaigall, 2020. "Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 437-465, May.
    2. Kosorok, Michael R., 2003. "Bootstraps of sums of independent but not identically distributed stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 299-318, February.
    3. Amengual, Dante & Carrasco, Marine & Sentana, Enrique, 2020. "Testing distributional assumptions using a continuum of moments," Journal of Econometrics, Elsevier, vol. 218(2), pages 655-689.
    4. Markevičiūtė, J., 2016. "Epidemic change tests for the mean of innovations of an AR(1) process," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 79-91.
    5. Bae, Jongsig & Hwang, Changha & Jun, Doobae, 2012. "The uniform central limit theorem for the tent map," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1021-1027.
    6. Quansheng Liu & Emmanuel Rio & Alain Rouault, 2003. "Limit Theorems for Multiplicative Processes," Journal of Theoretical Probability, Springer, vol. 16(4), pages 971-1014, October.

    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:117:y:2007:i:8:p:1137-1164. 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.