Some Results on the Brownian Meander with Drift

In this paper we study the drifted Brownian meander that is a Brownian motion starting from u and subject to the condition that min ≤z≤t B(z) > v with u> v. The limiting process for 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