@article{Yang2025, 
author = {Hui Yang},
title = {Large deviations for transient random walks with asymptotically zero drifts},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {8777-8793},
keywords = {nearest-neighbor, transient, random walk, large deviations, asymptotic perturbations},
url = {https://www.sciopen.com/article/10.3934/math.2025402},
doi = {10.3934/math.2025402},
abstract = {We consider transient nearest-neighbor random walks    X  :=  {      X          n            }          n      ≥      0       on the half-line, whose transition probabilities are state-dependent with certain asymptotic perturbations. This is a specific case of Lamperti's random walks. Let        M          t        :=  max  {      X          i        ,    0  ≤  i  ≤  t  } be the maximum process of    X, and        T          n        :=  inf  {  t  ≥  0  ,      X          t        =  n  } be its inverse process. Hong&Yang (2019) provided the law of large numbers for        T          n      . In this paper, we study the large deviations for        M          t       and        T          n       with speeds less than    n. This indicates that the perturbations slow down the random walk.}
}