Geodesic
Functional limit theorem for a stopped random walk attaining a high level
Diskretnaya Matematika, Tome 28 (2016) no. 3, pp. 3-13.

Voir la notice de l'article provenant de la source Math-Net.Ru

For a stopped random walk with zero drift conditioned to attain a high level the theorem on the convergence in distribution to the Brownian high jump in the space $D\left[ 0,+\infty \right) $ is proved.
Keywords: Brownian meander, Brownian excursion, Brownian high jump, stopped random walk, functional limit theorems. 
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V. I. Afanasyev. Functional limit theorem for a stopped random walk attaining a high level. Diskretnaya Matematika, Tome 28 (2016) no. 3, pp. 3-13. http://geodesic.mathdoc.fr/item/DM_2016_28_3_a0/

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