IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v90y2014icp149-154.html
   My bibliography  Save this article

On the use of the Borel–Cantelli lemma in Markov chains

Author

Listed:
  • Stepanov, Alexei

Abstract

In the present paper, we propose technical generalizations of the Borel–Cantelli lemma. These generalizations can be further used to derive strong limit results for Markov chains. In our work, we obtain some strong limit results.

Suggested Citation

  • Stepanov, Alexei, 2014. "On the use of the Borel–Cantelli lemma in Markov chains," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 149-154.
    • Handle: RePEc:eee:stapro:v:90:y:2014:i:c:p:149-154
    DOI: 10.1016/j.spl.2014.03.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715214001187
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2014.03.025?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. Bairamov, I. & Stepanov, A., 2011. "Numbers of near bivariate record-concomitant observations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 908-917, May.
    2. Petrov, Valentin V., 2002. "A note on the Borel-Cantelli lemma," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 283-286, July.
    3. Bairamov, I. & Stepanov, A., 2010. "Numbers of near-maxima for the bivariate case," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 196-205, February.
    4. Petrov, Valentin V., 2004. "A generalization of the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 233-239, April.
    5. Frolov, Andrei N., 2012. "Bounds for probabilities of unions of events and the Borel–Cantelli lemma," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2189-2197.
    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. Stepanov, Alexei & Berred, Alexandre & Nevzorov, Valery B., 2016. "Concomitants of records: Limit results, generation techniques, correlation," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 184-188.

    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. N. Balakrishnan & Alexei Stepanov, 2015. "Limit results for concomitants of order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 385-397, May.
    2. Xie, Yuquan, 2008. "A bilateral inequality on the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2052-2057, October.
    3. Frolov, Andrei N., 2012. "Bounds for probabilities of unions of events and the Borel–Cantelli lemma," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2189-2197.
    4. Stepanov, Alexei & Berred, Alexandre & Nevzorov, Valery B., 2016. "Concomitants of records: Limit results, generation techniques, correlation," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 184-188.
    5. Alexandre Berred & Alexei Stepanov, 2015. "Asymptotic properties of the number of near minimum-concomitant observations in the case of progressive type-II censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 283-294, April.
    6. Chandra, Tapas Kumar, 2008. "The Borel-Cantelli lemma under dependence conditions," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 390-395, March.
    7. Dembińska, Anna & Akbari, Masoumeh & Ahmadi, Jafar, 2021. "On numbers of observations in random regions determined by records for tail-less populations," Statistics & Probability Letters, Elsevier, vol. 179(C).
    8. Raúl Gouet & F. López & Gerardo Sanz, 2015. "On the point process of near-record values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 302-321, June.
    9. Bairamov, I. & Stepanov, A., 2011. "Numbers of near bivariate record-concomitant observations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 908-917, May.
    10. Pakhteev, A. & Stepanov, A., 2016. "Simulation of Gamma records," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 204-212.
    11. Dembinska, Anna & Iliopoulos, George, 2012. "On the asymptotics of numbers of observations in random regions determined by order statistics," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 151-160, January.
    12. Miguel Lafuente & Raúl Gouet & F. Javier López & Gerardo Sanz, 2022. "Near-Record Values in Discrete Random Sequences," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    13. Hu, Shuhe & Wang, Xuejun & Li, Xiaoqin & Zhang, Yuanyuan, 2009. "Comments on the paper: A bilateral inequality on the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 889-893, April.
    14. Pakhteev, A. & Stepanov, A., 2019. "Discrete records: Limit theorems for their spacings and generation methods," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 134-142.
    15. B. Prakasa Rao, 2009. "Conditional independence, conditional mixing and conditional association," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 441-460, June.
    16. Frolov, Andrei N., 2017. "On inequalities for values of first jumps of distribution functions and Hölder’s inequality," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 150-156.
    17. Bairamov, Ismihan & Khaledi, Baha-Eldin & Shaked, Moshe, 2014. "Stochastic comparisons of order statistics and their concomitants," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 105-115.
    18. Yang, Jun & Alajaji, Fady & Takahara, Glen, 2016. "On bounding the union probability using partial weighted information," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 38-44.
    19. Petrov, Valentin V., 2004. "A generalization of the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 233-239, April.
    20. Frolov, Andrei N., 2021. "On upper and lower bounds for probabilities of combinations of events," Statistics & Probability Letters, Elsevier, vol. 173(C).

    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:90:y:2014:i:c:p:149-154. 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.