2 citations · 3 across the 6 of their papers we have counts for
6 papers
Limit theorems for elephant random walks remembering the very recent past, with applications to the Takagi-van der Waerden class functions
Yuzaburo Nakano, Masato Takei
We study the Takagi-van der Waerden functions , a well-known class of continuous but nowhere differentiable functions, from probabilistic point of view. As an application…
Phase transitions for a unidirectional elephant random walk with a power law memory II: Some sharper estimates
Rahul Roy, Masato Takei, Hideki Tanemura
We continue our study of the unidirectional elephant random walk (uERW) initiated in {\it {Electron. Commun. Probab.}} ({\bf 29} 2024, article no. 78). In this paper we obtain defi…
A note on the long time behavior of the elephant random walk with stops
Tatsuya Akimoto, Masato Takei, Keisuke Taniguchi
We study the long time behavior of the elephant random walk with stops, introduced by Kumar, Harbola and Lindenberg (2010), and establish the phase transition of the number of visi…
How often can two independent elephant random walks on meet?
Rahul Roy, Masato Takei, Hideki Tanemura
We show that two independent elephant random walks on the integer lattice meet each other finitely often or infinitely often depends on whether the memory parameter $p…
The elephant random walk in the triangular array setting
Rahul Roy, Masato Takei, Hideki Tanemura
Gut and Stadmüller (2021, 2022) initiated the study of the elephant random walk with limited memory. Aguech and El Machkouri (2024) published a paper in which they discuss an exten…
Phase transitions for a unidirectional elephant random walk with a power law memory
Rahul Roy, Masato Takei, Hideki Tanemura
For the standard elephant random walk, Laulin (2022) studied the case when the increment of the random walk is not uniformly distributed over the past history instead has a power l…