Some results on the Brownian meander with drift

Francesco Iafrate; Enzo Orsingher

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arXiv · 1710.02350

Some results on the Brownian meander with drift

Francesco Iafrate·Enzo Orsingher

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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\leq z \leq t} B(z)> v $ with $ u > v $. The limiting process for $ u \downarrow v $ is analyzed 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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Francesco Iafrate, Enzo Orsingher. 2017-10-06. Some results on the Brownian meander with drift. https://arxiv.org/abs/1710.02350

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