In this paper, we explain the connection between the elephant random walk (ERW) and an
urn model à la Pólya and derive functional limit theorems for the former. The ERW model …

The purpose of this paper is to establish, via a martingale approach, some refinements on
the asymptotic behavior of the one-dimensional elephant random walk (ERW). The …

In this work, we consider stochastic movement with random resets to the origin followed by a
random residence time before the motion starts again. First, we study the transport …

One class of random walks with infinite memory, so-called elephant random walks, are
simple models describing anomalous diffusion. We present a surprising connection between …

The purpose of this paper is to investigate the asymptotic behavior of the multi-dimensional
elephant random walk (MERW). It is a non-Markovian random walk which has a complete …

Motivated by recent interest in the stochastic resetting of a random walker, we propose a
generalized model where the random walker takes stochastic jumps of lengths proportional …

Many man-made and natural processes involve the diffusion of microscopic particles subject
to random or chaotic, random-like movements. Besides the normal diffusion characterized …

The discrete stochastic dynamics of a random walker in the presence of resetting and
memory is analyzed. Resetting and memory effects may compete in certain parameter …

We consider a minimal model of one-dimensional discrete-time random walk with step-
reinforcement, introduced by Harbola, Kumar, and Lindenberg (2014): The walker can move …

The aim of this paper is to go further in the analysis of the asymptotic behavior of the so-
called minimal random walk (MRW) using a new martingale approach. The MRW is a …