Abstract
Abstract
The elephant random walk (ERW) is a discrete-time random walk introduced by Schütz and Trimper (2004) in order to investigate how long-range memory affects the behavior of the random walk. Its particularity is that the next step of the walker depends on its whole past through a parameter
p
∈
[
0
,
1
]
. In this work, we investigate the validity of the central limit theorem of the ERW when the walker has only a gradually increasing memory. Our contribution provides a positive answer to a conjecture raised in a recent work by Gut and Stadtmüller (2022 Stat. Probab. Lett.
189 109598).
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics