Some Results on the Brownian Meander with Drift

  • F. Iafrate
  • E. OrsingherEmail author


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.


Tightness Weak convergence First-passage times Absorbing drifted Brownian motion Drifted Brownian excursion 

Mathematics Subject Classification (2010)

60G17 60J65 



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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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Sapienza, University of RomeRomeItaly

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