IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v53y1994i1p147-173.html
   My bibliography  Save this article

Properties of the telegrapher's random process with or without a trap

Author

Listed:
  • Foong, S. K.
  • Kanno, S.

Abstract

The properties of the telegrapher random process which is a Poissonian random walk on a straight line are studied in detail in probabilistic terms. The paper contains, besides the details of a rapid communication (Foong, 1992) by one of the authors, a number of new results. The distributions of the first passage time subject to an arbitrary number of reversals in the walk are obtained explicitly for both the starting directions. These distributions are then used to obtain, again explicitly, the corresponding distributions of the maximum of the walk, proving the conjecture by Orsingher (1990) for the one started moving right. The densities of the displacements from the origin in the presence of a trap are also given in detail. The relationship between this density and (1) the first passage time and (2) the maximum are given.

Suggested Citation

  • Foong, S. K. & Kanno, S., 1994. "Properties of the telegrapher's random process with or without a trap," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 147-173, September.
    • Handle: RePEc:eee:spapps:v:53:y:1994:i:1:p:147-173
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(94)90061-2
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Igor G. Pospelov & Stanislav A. Radionov, 2015. "Optimal Dividend Policy When Cash Surplus Follows The Telegraph Process," HSE Working papers WP BRP 48/FE/2015, National Research University Higher School of Economics.
    2. De Gregorio, Alessandro & Macci, Claudio, 2012. "Large deviation principles for telegraph processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1874-1882.
    3. De Gregorio, Alessandro & Iafrate, Francesco, 2021. "Telegraph random evolutions on a circle," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 79-108.
    4. Soham Biswas & Francois Leyvraz, 2021. "Ballistic annihilation in one dimension: a critical review," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(12), pages 1-10, December.
    5. Kolesnik, Alexander D. & Turbin, Anatoly F., 1998. "The equation of symmetric Markovian random evolution in a plane," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 67-87, June.
    6. Bogachev, Leonid & Ratanov, Nikita, 2011. "Occupation time distributions for the telegraph process," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1816-1844, August.
    7. Nikita Ratanov, 2020. "First Crossing Times of Telegraph Processes with Jumps," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 349-370, March.
    8. 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.
    9. Iuliano, Antonella & Macci, Claudio, 2023. "Asymptotic results for the absorption time of telegraph processes with a non-standard barrier at the origin," Statistics & Probability Letters, Elsevier, vol. 196(C).
    10. Mazza, Christian & Rulliere, Didier, 2004. "A link between wave governed random motions and ruin processes," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 205-222, October.
    11. Ratanov, Nikita, 2021. "On telegraph processes, their first passage times and running extrema," Statistics & Probability Letters, Elsevier, vol. 174(C).
    12. Iacus, Stefano Maria, 2001. "Statistical analysis of the inhomogeneous telegrapher's process," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 83-88, November.
    13. Jiang Hui & Xu Lihu & Yang Qingshan, 2024. "Functional Large Deviations for Kac–Stroock Approximation to a Class of Gaussian Processes with Application to Small Noise Diffusions," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3015-3054, November.
    14. Cinque, Fabrizio, 2022. "A note on the conditional probabilities of the telegraph process," Statistics & Probability Letters, Elsevier, vol. 185(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:spapps:v:53:y:1994:i:1:p:147-173. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.