Author:
Liu Yuelin,Sidoravicius Vladas,Wang Longmin,Xiang Kainan
Abstract
AbstractWe establish an invariance principle and a large deviation principle for a biased random walk
${\text{RW}}_\lambda$
with
$\lambda\in [0,1)$
on
$\mathbb{Z}^d$
. The scaling limit in the invariance principle is not a d-dimensional Brownian motion. For the large deviation principle, its rate function is different from that of a drifted random walk, as may be expected, though the reflected biased random walk evolves like the drifted random walk in the interior of the first quadrant and almost surely visits coordinate planes finitely many times.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability