Some Results on the Brownian Meander with Drift

F. Iafrate () and E. Orsingher ()
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F. Iafrate: Sapienza, University of Rome
E. Orsingher: Sapienza, University of Rome

Journal of Theoretical Probability, 2020, vol. 33, issue 2, 1034-1060

Abstract: Abstract In this paper we study the drifted Brownian meander that is a Brownian motion starting from u and subject to the condition that $$ \min _{ 0\le z \le t} B(z)> v $$min0≤z≤tB(z)>v with $$ u > v $$u>v. The limiting process for $$ u \downarrow v $$u↓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.

Keywords: Tightness; Weak convergence; First-passage times; Absorbing drifted Brownian motion; Drifted Brownian excursion; 60G17; 60J65 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00891-3

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