IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v138y2018icp47-56.html
   My bibliography  Save this article

Large deviations for some logarithmic means in the case of random variables with thin tails

Author

Listed:
  • Giuliano, Rita
  • Macci, Claudio

Abstract

In this paper we generalize Theorem 3.3 in Giuliano and Macci (2011). More precisely we prove the full large deviation principle without assuming a particular condition in that theorem and, moreover, we give some results for the case of random variables with thin tails (and not super-exponential tails). As an application we deduce some consequences for the logarithmic means of some random variables expressed in terms of a C-process.

Suggested Citation

  • Giuliano, Rita & Macci, Claudio, 2018. "Large deviations for some logarithmic means in the case of random variables with thin tails," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 47-56.
    • Handle: RePEc:eee:stapro:v:138:y:2018:i:c:p:47-56
    DOI: 10.1016/j.spl.2018.02.066
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715218301111
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2018.02.066?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. Fahrner, I. & Stadtmüller, U., 1998. "On almost sure max-limit theorems," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 229-236, March.
    2. Fahrner, Ingo, 2000. "An extension of the almost sure max-limit theorem," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 93-103, August.
    3. Berkes, István & Csáki, Endre, 2001. "A universal result in almost sure central limit theory," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 105-134, July.
    4. Heck, Matthias K., 1998. "The principle of large deviations for the almost everywhere central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 61-75, August.
    5. Lifshits, M. A. & Stankevich, E. S., 2001. "On the large deviation principle for the almost sure CLT," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 263-267, February.
    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. Giuliano, Rita & Macci, Claudio & Pacchiarotti, Barbara, 2019. "Large deviations for weighted means of random vectors defined in terms of suitable Lévy processes," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 13-22.

    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. Giuliano, Rita & Macci, Claudio & Pacchiarotti, Barbara, 2019. "Large deviations for weighted means of random vectors defined in terms of suitable Lévy processes," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 13-22.
    2. Stadtmüller, U., 2002. "Almost sure versions of distributional limit theorems for certain order statistics," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 413-426, July.
    3. Tan, Zhongquan & Peng, Zuoxiang, 2009. "Almost sure convergence for non-stationary random sequences," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 857-863, April.
    4. Luísa Pereira & Zhongquan Tan, 2017. "Almost Sure Convergence for the Maximum of Nonstationary Random Fields," Journal of Theoretical Probability, Springer, vol. 30(3), pages 996-1013, September.
    5. Berkes, István, 2001. "The law of large numbers with exceptional sets," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 431-438, December.
    6. Csáki, Endre & Gonchigdanzan, Khurelbaatar, 2002. "Almost sure limit theorems for the maximum of stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 195-203, June.
    7. Zhicheng Chen & Hongyun Zhang & Xinsheng Liu, 2020. "Almost Sure Convergence for the Maximum and Minimum of Normal Vector Sequences," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    8. Fahrner, Ingo, 2001. "A strong invariance principle for the logarithmic average of sample maxima," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 317-337, June.
    9. Berkes, István & Weber, Michel, 2006. "Almost sure versions of the Darling-Erdös theorem," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 280-290, February.
    10. Panga, Zacarias & Pereira, Luísa, 2019. "On the almost sure convergence for the joint version of maxima and minima of stationary sequences," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    11. Berkes, István & Csáki, Endre & Csörgo, Sándor, 1999. "Almost sure limit theorems for the St. Petersburg game," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 23-30, October.
    12. Hashorva, Enkelejd & Weng, Zhichao, 2013. "Limit laws for extremes of dependent stationary Gaussian arrays," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 320-330.
    13. Bercu, B., 2004. "On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 157-173, May.
    14. Holzmann, Hajo & Koch, Susanne & Min, Aleksey, 2004. "Almost sure limit theorems for U-statistics," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 261-269, September.
    15. István Fazekas & Alexey Chuprunov, 2007. "An Almost Sure Functional Limit Theorem for the Domain of Geometric Partial Attraction of Semistable Laws," Journal of Theoretical Probability, Springer, vol. 20(2), pages 339-353, June.
    16. Alain Rouault & Marc Yor & Marguerite Zani, 2002. "A Large Deviations Principle Related to the Strong Arc-Sine Law," Journal of Theoretical Probability, Springer, vol. 15(3), pages 793-815, July.
    17. Wang, Jiang-Feng & Liang, Han-Ying, 2008. "A note on the almost sure central limit theorem for negatively associated fields," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1964-1970, September.
    18. Tan, Zhongquan, 2013. "An almost sure limit theorem for the maxima of smooth stationary Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2135-2141.
    19. István Berkes & Siegfried Hörmann & Lajos Horváth, 2010. "On Functional Versions of the Arc-Sine Law," Journal of Theoretical Probability, Springer, vol. 23(1), pages 109-126, March.
    20. Bercu, Bernard & Nourdin, Ivan & Taqqu, Murad S., 2010. "Almost sure central limit theorems on the Wiener space," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1607-1628, August.

    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:138:y:2018:i:c:p:47-56. 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.