IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v361y2019icp617-629.html
   My bibliography  Save this article

Goldstein-Kac telegraph equations and random flights in higher dimensions

Author

Listed:
  • Pogorui, Anatoliy A.
  • Rodríguez-Dagnino, Ramón M.

Abstract

In this paper we deal with random motions in dimensions two, three, and five, where the governing equations are telegraph-type equations in these dimensions. Our methodology is first applied to the second-order telegraph equation and we refine well-known results found by other methods. Next, we show that the (2,λ)-Erlang distribution for sojourn times defines the underlying stochastic process for the three-dimensional Goldstein-Kac type telegraph equation and by finding the corresponding fundamental solution of this equation, we have obtained the approximated expression for the transition density of the three-dimensional movement, our results are more complete than previous ones, and this result may have important consequences in applications. We also obtain the 5-dimensional telegraph-type equation by assuming a random motion with an (4,λ)-Erlang distribution for sojourn times, and such equation can be factorized as the product of two telegraph-type equations where one of them is the Goldstein-Kac 5-dimensional telegraph equation. In our analysis the dimension n is related to the (n−1,λ)-Erlang distribution for sojourn times of the random walks.

Suggested Citation

  • Pogorui, Anatoliy A. & Rodríguez-Dagnino, Ramón M., 2019. "Goldstein-Kac telegraph equations and random flights in higher dimensions," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 617-629.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:617-629
    DOI: 10.1016/j.amc.2019.05.045
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319304473
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.05.045?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. Pogorui, Anatoliy A. & Rodríguez-Dagnino, Ramón M., 2013. "Random motion with gamma steps in higher dimensions," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1638-1643.
    2. De Gregorio, Alessandro & Orsingher, Enzo, 2012. "Flying randomly in Rd with Dirichlet displacements," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 676-713.
    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. De Gregorio, Alessandro, 2017. "A note on isotropic random flights moving in mixed Poisson environments," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 311-317.
    2. Le Caër, Gérard, 2015. "Two-step Dirichlet random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 201-215.
    3. Pogorui, Anatoliy A. & Rodríguez-Dagnino, Ramón M., 2013. "Random motion with gamma steps in higher dimensions," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1638-1643.
    4. De Gregorio, Alessandro, 2016. "Transport processes with random jump rate," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 127-134.
    5. Cinque, Fabrizio & Orsingher, Enzo, 2021. "On the exact distributions of the maximum of the asymmetric telegraph process," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 601-633.

    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:apmaco:v:361:y:2019:i:c:p:617-629. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.