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Asymptotic results for the absorption time of telegraph processes with a non-standard barrier at the origin

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  • Iuliano, Antonella
  • Macci, Claudio

Abstract

A telegraph process with an elastic barrier at the origin was studied in Di Crescenzo et al. (2018); in particular the number of visits of the origin before the absorption is a geometric distributed random variable M. Some asymptotic results (large and moderate deviations) for that model were obtained in Macci et al. (2021). In this paper we study large and moderate deviations for a generalized model where M is a light-tailed distributed random variable.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:196:y:2023:i:c:s016771522300024x
    DOI: 10.1016/j.spl.2023.109800
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Claudio Macci & Barbara Martinucci & Enrica Pirozzi, 2021. "Asymptotic Results for the Absorption Time of Telegraph Processes with Elastic Boundary at the Origin," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1077-1096, September.
    4. Macci, Claudio, 2016. "Large deviations for some non-standard telegraph processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 119-127.
    5. 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.
    6. 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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