IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v120y2010i7p1178-1193.html
   My bibliography  Save this article

On the probability that integrated random walks stay positive

Author

Listed:
  • Vysotsky, Vladislav

Abstract

Let Sn be a centered random walk with a finite variance, and consider the sequence , which we call an integrated random walk. We are interested in the asymptotics of as N-->[infinity]. Sinai (1992) [15] proved that pN[asymptotically equal to]N-1/4 if Sn is a simple random walk. We show that pN[asymptotically equal to]N-1/4 for some other kinds of random walks that include double-sided exponential and double-sided geometric walks, both not necessarily symmetric. We also prove that pN 0) is an exponential distribution.

Suggested Citation

  • Vysotsky, Vladislav, 2010. "On the probability that integrated random walks stay positive," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1178-1193, July.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:7:p:1178-1193
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00074-8
    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. Drmota, Michael & Marckert, Jean-François, 2005. "Reinforced weak convergence of stochastic processes," Statistics & Probability Letters, Elsevier, vol. 71(3), pages 283-294, March.
    2. de Haan, L. & Omey, E. & Resnick, S., 1984. "Domains of attraction and regular variation in IRd," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 17-33, February.
    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. Yun, Seokhoon, 1997. "On Domains of Attraction of Multivariate Extreme Value Distributions under Absolute Continuity," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 277-295, November.
    2. Peng, Liang, 2002. "Asymptotic expansions of densities of sums of random vectors without third moment," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 167-174, June.
    3. Tiandong Wang & Sidney I. Resnick, 2018. "Multivariate Regular Variation of Discrete Mass Functions with Applications to Preferential Attachment Networks," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 1029-1042, September.
    4. Omey, Edward & Vesilo, R., 2009. "Random Sums of Random Variables and Vectors," Working Papers 2009/09, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    5. Mallor, F. & Omey, E. & Santos, J., 2007. "Multivariate weighted renewal functions," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 30-39, January.

    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:120:y:2010:i:7:p:1178-1193. 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.