Abstract
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→∞, towards the Brownian meander.
Original language | English |
---|---|
Pages (from-to) | 3313-3350 |
Journal | Annals of Probability |
Volume | 46 |
Issue number | 6 |
Early online date | 25 Sep 2018 |
DOIs | |
Publication status | Published - 2018 |