In this paper we study the drifted Brownian meander that is a Brownian motion starting from u and subject to the condition that $$ \min _{ 0\le z \le t} B(z)> v $$ min 0 ≤ z ≤ t B ( 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.

中文翻译：

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带有漂移的布朗河曲的一些结果

在本文中，我们研究漂移布朗曲流，它是从 u 开始的布朗运动，并服从于 $$ \min _{ 0\le z \le t} B(z)> v $$ min 0 ≤ z ≤ t B ( z ) > v 与 $$ u > v $$ u > v 。分析了$$ u \downarrow v $$ u ↓ v 的极限过程，给出了其构造的充分条件。我们还研究了具有漂移的曲流最大值的分布和相关的首次通过时间。提供了具有漂移的曲流的表示，并扩展了无漂移情况的众所周知的结果。最后一部分涉及漂移的偏移过程，其分布与无漂移的情况相吻合。