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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
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    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)

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