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Approximation of the first passage time distribution for the birth-death processes

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  • Aleksejus Kononovicius
  • Vygintas Gontis

Abstract

We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain closed-form expressions. We apply the method to the three selected birth-death processes and the sophisticated order-book model exhibiting long-range memory. We discuss how our approach contributes to the competition between spurious and true long-range memory models.

Suggested Citation

  • Aleksejus Kononovicius & Vygintas Gontis, 2019. "Approximation of the first passage time distribution for the birth-death processes," Papers 1902.00924, arXiv.org.
    • Handle: RePEc:arx:papers:1902.00924
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    Cited by:

    1. Gontis, V. & Kononovicius, A., 2020. "Bessel-like birth–death process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. Park, Seong Jun & Choi, M.Y., 2024. "Analytic expression of the probability density function for the first-passage time in birth-death processes," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    3. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.
    4. Vygintas Gontis & Aleksejus Kononovicius, 2019. "Bessel-like birth-death process," Papers 1904.13064, arXiv.org, revised Oct 2019.

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