IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v50y2000i3p305-312.html
   My bibliography  Save this article

Strong laws for the maximal gain over increasing runs

Author

Listed:
  • Frolov, Andrei
  • Martikainen, Alexander
  • Steinebach, Josef

Abstract

Let {(Xi,Yi)}i=1,2,... be an i.i.d. sequence of bivariate random vectors with P(Y1=y)=0 for all y. Put Mn=Mn(Ln)=max0[less-than-or-equals, slant]k[less-than-or-equals, slant]n-Ln(Xk+1+...+Xk+Ln)Ik,Ln, where Ik,l=I{Yk+1[less-than-or-equals, slant]...[less-than-or-equals, slant]Yk+l} denotes the indicator function of the event in brackets, Ln is the largest l[less-than-or-equals, slant]n, for which Ik,l=1 for some k=0,1,...,n-l. If, for example, Xi=Yi, i[greater-or-equal, slanted]1, and Xi denotes the gain in the ith repetition of a game of chance, then Mn is the maximal gain over increasing runs of maximal length Ln. We derive a strong law of large numbers and a law of iterated logarithm type result for Mn.

Suggested Citation

  • Frolov, Andrei & Martikainen, Alexander & Steinebach, Josef, 2000. "Strong laws for the maximal gain over increasing runs," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 305-312, November.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:3:p:305-312
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(00)00119-X
    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. Frolov, Andrei N., 1998. "On one-sided strong laws for large increments of sums," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 155-165, February.
    2. Frolov, Andrei N. & Martikainen, Alexander I., 1999. "On the length of the longest increasing run in d," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 153-161, January.
    3. Révész, P., 1983. "Three problems on the lengths of increasing runs," Stochastic Processes and their Applications, Elsevier, vol. 15(2), pages 169-179, July.
    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. Frolov, Andrei N., 2003. "On asymptotics of the maximal gain without losses," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 13-23, May.

    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. Frolov, Andrei N., 2003. "On asymptotics of the maximal gain without losses," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 13-23, May.
    2. Frolov, Andrei N., 2005. "Converses to the Csörgo-Révész laws," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 113-123, April.
    3. Nathalie Mitton & Katy Paroux & Bruno Sericola & Sébastien Tixeuil, 2010. "Ascending Runs in Dependent Uniformly Distributed Random Variables: Application to Wireless Networks," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 51-62, March.
    4. Alexandru Amarioarei & Cristian Preda, 2020. "One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems," Mathematics, MDPI, vol. 8(4), pages 1-11, April.

    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:50:y:2000:i:3:p:305-312. 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.