Denisov, Denis et al., First-passage times for random walks with nonidentically distributed increments, Annals of probability (Online) , 46(6), 2018, pp. 3313-3350
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.