IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v14y2001i2d10.1023_a1011107629319.html
   My bibliography  Save this article

The Length of the Longest Head-Run in a Model with Long Range Dependence

Author

Listed:
  • Thomas M. Lewis

    (Furman University)

Abstract

In this paper, we construct stationary sequences of random variables {χ i : i≥0} taking values ±1 with probability 1/2 and we prove an Erdös–Rényi law of large numbers for the length of the longest run of consecutive +1's in the sample {χ0,..., χ n }. Our model, which is called random walk in random scenery, exhibits long-range, positive dependence.

Suggested Citation

  • Thomas M. Lewis, 2001. "The Length of the Longest Head-Run in a Model with Long Range Dependence," Journal of Theoretical Probability, Springer, vol. 14(2), pages 357-378, April.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:2:d:10.1023_a:1011107629319
    DOI: 10.1023/A:1011107629319
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1011107629319
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1011107629319?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. Khoshnevisan, Davar & Lewis, Thomas M., 1998. "A law of the iterated logarithm for stable processes in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 89-121, May.
    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. Zhang, Li-Xin, 2001. "The strong approximation for the Kesten-Spitzer random walk," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 21-26, May.
    2. Wendler, Martin, 2016. "The sequential empirical process of a random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2787-2799.
    3. Chen, Xia & Rosen, Jay, 2010. "Large deviations and renormalization for Riesz potentials of stable intersection measures," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1837-1878, August.
    4. Chen, Xia, 2006. "Self-intersection local times of additive processes: Large deviation and law of the iterated logarithm," Stochastic Processes and their Applications, Elsevier, vol. 116(9), pages 1236-1253, September.
    5. Révész, Pál & Shi, Zhan, 2000. "Strong approximation of spatial random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 329-345, August.
    6. Csáki, Endre & König, Wolfgang & Shi, Zhan, 1999. "An embedding for the Kesten-Spitzer random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 283-292, August.
    7. Csáki, Endre & Révész, Pál & Shi, Zhan, 2001. "A strong invariance principle for two-dimensional random walk in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 181-200, April.
    8. Deuschel, Jean-Dominique & Fukushima, Ryoki, 2019. "Quenched tail estimate for the random walk in random scenery and in random layered conductance," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 102-128.
    9. N. Guillotin-Plantard, 2001. "Dynamic ℤ d -Random Walks in a Random Scenery: A Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 14(1), pages 241-260, January.
    10. Guillotin-Plantard, Nadine & Poisat, Julien, 2013. "Quenched central limit theorems for random walks in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1348-1367.

    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:spr:jotpro:v:14:y:2001:i:2:d:10.1023_a:1011107629319. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.