First-passage times for random walks with nonidentically distributed increments

@article{Denisov2018FirstpassageTF,
title={First-passage times for random walks with nonidentically distributed increments},
author={Denis Denisov and Alexander I. Sakhanenko and Vitali Wachtel},
journal={The Annals of Probability},
year={2018}
}
• Published 2 November 2016
• Mathematics
• The Annals of Probability
We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first-passage times over moving boundaries. Furthermore, we prove that a properly rescaled random walk conditioned to stay above the boundary up to time $n$ converges, as $n\to\infty$, towards the Brownian meander.

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