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Simulation of First-Passage Times for Alternating Brownian Motions

Author

Listed:
  • A. Crescenzo

    (Università di Salerno)

  • E. Nardo

    (Università degli Studi della Basilicata)

  • L. M. Ricciardi

    (Università di Napoli Federico II)

Abstract

The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by an alternating renewal process. Bounds to the first-passage-time density and distribution function are obtained, and a simulation procedure to estimate first-passage-time densities is constructed. Examples of applications to problems in environmental sciences and mathematical finance are also provided.

Suggested Citation

  • A. Crescenzo & E. Nardo & L. M. Ricciardi, 2005. "Simulation of First-Passage Times for Alternating Brownian Motions," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 161-181, June.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:2:d:10.1007_s11009-005-1481-3
    DOI: 10.1007/s11009-005-1481-3
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    References listed on IDEAS

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    1. David Cyranoski, 2000. "Swimming against the tide," Nature, Nature, vol. 408(6814), pages 764-766, December.
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    Cited by:

    1. Vladimir Pozdnyakov & L. Mark Elbroch & Anthony Labarga & Thomas Meyer & Jun Yan, 2019. "Discretely Observed Brownian Motion Governed by Telegraph Process: Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 907-920, 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.

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