On the sojourn time of a generalized Brownian meander

F. Iafrate and E. Orsingher

Statistics & Probability Letters, 2021, vol. 168, issue C

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.

Keywords: Drifted Brownian meander; Brownian excursion; Feynman–Kac functional; Weak convergence; Tightness; Elastic Brownian motion (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2020.108927

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