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Probabilistic analysis of the telegrapher's process with drift by means of relativistic transformations

Author

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  • L. Beghin
  • L. Nieddu
  • E. Orsingher

Abstract

The telegrapher's process with drift is here examined and its distribution is obtained by applying the Lorentz transformation. The related characteristic function as well as the distribution are also derived by solving an initial value problem for the generalized telegraph equation.

Suggested Citation

  • L. Beghin & L. Nieddu & E. Orsingher, 2001. "Probabilistic analysis of the telegrapher's process with drift by means of relativistic transformations," International Journal of Stochastic Analysis, Hindawi, vol. 14, pages 1-15, January.
    • Handle: RePEc:hin:jnijsa:602054
    DOI: 10.1155/S104895330100003X
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    Citations

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    Cited by:

    1. Antonio Crescenzo & Barbara Martinucci & Paola Paraggio & Shelemyahu Zacks, 2021. "Some Results on the Telegraph Process Confined by Two Non-Standard Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 837-858, September.
    2. Antonio Di Crescenzo & Barbara Martinucci, 2013. "On the Generalized Telegraph Process with Deterministic Jumps," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 215-235, March.
    3. 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.
    4. De Gregorio, Alessandro & Iafrate, Francesco, 2021. "Telegraph random evolutions on a circle," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 79-108.
    5. Anatoliy Pogorui & Anatoly Swishchuk & Ramón M. Rodríguez-Dagnino & Alexander Sarana, 2023. "Cox-Based and Elliptical Telegraph Processes and Their Applications," Risks, MDPI, vol. 11(7), pages 1-15, July.
    6. Nikita Ratanov, 2021. "Ornstein-Uhlenbeck Processes of Bounded Variation," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 925-946, September.
    7. Ratanov, Nikita, 2021. "On telegraph processes, their first passage times and running extrema," Statistics & Probability Letters, Elsevier, vol. 174(C).
    8. 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.
    9. Cinque, Fabrizio, 2022. "A note on the conditional probabilities of the telegraph process," Statistics & Probability Letters, Elsevier, vol. 185(C).
    10. Antonio Di Crescenzo & Barbara Martinucci & Shelemyahu Zacks, 2018. "Telegraph Process with Elastic Boundary at the Origin," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 333-352, March.

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