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On the sojourn time of a generalized Brownian meander

Author

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  • Iafrate, F.
  • Orsingher, E.

Abstract

In this paper we study the sojourn time on the positive half-line up to time t of a drifted Brownian motion with starting point u and subject to the condition that min0≤z≤lB(z)>v, with u>v. This process is a drifted Brownian meander up to time l and then evolves as a free Brownian motion. We also consider the sojourn time of a bridge-type process, where we add the additional condition to return to the initial level at the end of the time interval. We analyze the weak limit of the occupation functional as u↓v. We obtain explicit distributional results when the barrier is placed at the zero level, and also in the special case when the drift is null.

Suggested Citation

  • Iafrate, F. & Orsingher, E., 2021. "On the sojourn time of a generalized Brownian meander," Statistics & Probability Letters, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:stapro:v:168:y:2021:i:c:s0167715220302303
    DOI: 10.1016/j.spl.2020.108927
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    References listed on IDEAS

    as
    1. Nikitin, Yakov & Orsingher, Enzo, 2000. "The intermediate arc-sine law," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 119-125, August.
    2. Beghin, L. & Nikitin, Y. & Orsingher, E., 2003. "How the sojourn time distributions of Brownian motion are affected by different forms of conditioning," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 291-302, December.
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    Cited by:

    1. D’Ovidio, Mirko & Iafrate, Francesco, 2024. "Elastic drifted Brownian motions and non-local boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

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