First-passage times for random walks with non-identically distributed\n increments

2016/11/02 by Denis Denisov, Denisov, Denis, A. I. Sakhanenko +3 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #60G50 #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1611.00493

openalex publication_date 2016/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider random walks with independent but not necessarily identical\ndistributed increments. Assuming that the increments satisfy the well-known\nLindeberg condition, we investigate the asymptotic behaviour of first-passage\ntimes over moving boundaries. Furthermore, we prove that a properly rescaled\nrandom walk conditioned to stay above the boundary up to time n converges, as\nn\→\∞, towards the Brownian meander.\n

Citations

• Random walks conditioned to stay in Weyl chambers of type C and D

Cited by

• Random walks in Weyl chambers
• First-passage time asymptotics over moving boundaries for random walk bridges

Related

• First-passage times over moving boundaries for asymptotically stable walks
• First-passage times for random walks in the triangular array setting
• First-passage time asymptotics over moving boundaries for random walk bridges
• A note on the times of first passage for `nearly right-continuous'\n random walks
• Random walks and Brownian motion: A method of computation for first-passage times and related quantities in confined geometries