IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i4p934-d1066064.html
   My bibliography  Save this article

On Local Time for Telegraph Processes

Author

Listed:
  • Nikita Ratanov

    (Department of Mathematical Analysis, Chelyabinsk State University, 454001 Chelyabinsk, Russia)

  • Mikhail Turov

    (Department of Mathematical Analysis, Chelyabinsk State University, 454001 Chelyabinsk, Russia)

Abstract

The article consists of an introduction into the theory of passage times associated with telegraph processes. Local time for the telegraph process is defined and analysed. We provide some limited results for telegraphic local times.

Suggested Citation

  • Nikita Ratanov & Mikhail Turov, 2023. "On Local Time for Telegraph Processes," Mathematics, MDPI, vol. 11(4), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:934-:d:1066064
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/4/934/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/4/934/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Weam Alharbi & Sergei Petrovskii, 2018. "Critical Domain Problem for the Reaction–Telegraph Equation Model of Population Dynamics," Mathematics, MDPI, vol. 6(4), pages 1-15, April.
    2. Cinque, Fabrizio, 2022. "A note on the conditional probabilities of the telegraph process," Statistics & Probability Letters, Elsevier, vol. 185(C).
    3. Nikita Ratanov, 2007. "A jump telegraph model for option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 575-583.
    4. Weiss, George H, 2002. "Some applications of persistent random walks and the telegrapher's equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 381-410.
    5. Ratanov, Nikita, 2021. "On telegraph processes, their first passage times and running extrema," Statistics & Probability Letters, Elsevier, vol. 174(C).
    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. Nikita Ratanov, 2022. "Kac-Ornstein-Uhlenbeck Processes: Stationary Distributions and Exponential Functionals," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2703-2721, December.
    2. 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.
    3. Nikita Ratanov, 2004. "Branching random motions, nonlinear hyperbolic systems and traveling waves," Borradores de Investigación 4331, Universidad del Rosario.
    4. Jonathan R. Potts, 2019. "Directionally Correlated Movement Can Drive Qualitative Changes in Emergent Population Distribution Patterns," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
    5. López, Oscar & Oleaga, Gerardo & Sánchez, Alejandra, 2021. "Markov-modulated jump-diffusion models for the short rate: Pricing of zero coupon bonds and convexity adjustment," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    6. Cvetićanin, Stevan M. & Zorica, Dušan & Rapaić, Milan R., 2021. "Non-local telegrapher’s equation as a transmission line model," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    7. García-Pelayo, Ricardo, 2007. "Solution of the persistent, biased random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 143-149.
    8. López, Oscar & Ratanov, Nikita, 2012. "Kac’s rescaling for jump-telegraph processes," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1768-1776.
    9. Vallois, Pierre & Tapiero, Charles S., 2009. "A claims persistence process and insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 367-373, June.
    10. Nikita Ratanov, 2021. "Ornstein-Uhlenbeck Processes of Bounded Variation," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 925-946, September.
    11. Alessandro De Gregorio & Stefano Iacus, 2007. "Change point estimation for the telegraph process observed at discrete times," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1053, Universitá degli Studi di Milano.
    12. Ratanov, Nikita, 2014. "On piecewise linear processes," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 60-67.
    13. Nikita Ratanov & Alexander Melnikov, 2007. "On Financial Markets Based on Telegraph Processes," Papers 0712.3428, arXiv.org.
    14. Nikita Ratanov, 2016. "Option Pricing Under Jump-Diffusion Processes with Regime Switching," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 829-845, September.
    15. García-Pelayo, Ricardo, 2023. "New techniques to solve the 1-dimensional random flight," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    16. Antonio Di Crescenzo & Shelemyahu Zacks, 2015. "Probability Law and Flow Function of Brownian Motion Driven by a Generalized Telegraph Process," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 761-780, September.
    17. Awad, Emad, 2019. "On the time-fractional Cattaneo equation of distributed order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 210-233.
    18. Kolesnik, Alexander D., 2018. "Slow diffusion by Markov random flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 186-197.
    19. 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.
    20. Enzo Orsingher & Manfred Marvin Marchione, 2025. "Planar Random Motions in a Vortex," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-42, March.

    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:gam:jmathe:v:11:y:2023:i:4:p:934-:d:1066064. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.