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.
|Journal||Annals of Probability|
|Early online date||25 Sep 2018|
|Publication status||Published - 2018|