Abstract
In this paper we study the drifted Brownian meander that is a Brownian motion starting from u and subject to the condition that \( \min _{ 0\le z \le t} B(z)> v \) with \( u > v \). The limiting process for \( u \downarrow v \) is analysed, and the sufficient conditions for its construction are given. We also study the distribution of the maximum of the meander with drift and the related first-passage times. The representation of the meander endowed with a drift is provided and extends the well-known result of the driftless case. The last part concerns the drifted excursion process the distribution of which coincides with the driftless case.
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We thank both referees for their accuracy in the analysis of the first draft of this paper. They have detected misprints and errors, and their constructive criticism has substantially improved the paper.
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Iafrate, F., Orsingher, E. Some Results on the Brownian Meander with Drift. J Theor Probab 33, 1034–1060 (2020). https://doi.org/10.1007/s10959-019-00891-3
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DOI: https://doi.org/10.1007/s10959-019-00891-3
Keywords
- Tightness
- Weak convergence
- First-passage times
- Absorbing drifted Brownian motion
- Drifted Brownian excursion