arXiv subjects
Publications and source records attributed to Shuhei Shibata.
This paper investigates functional limit theorems for the Elephant Random Walk (ERW) on general periodic structures, extending the Bertenghi's results on $\mathbb{Z}^d$. Our results reveal new structure-dependent quantities that do not appear in the classical setting $\mathbb{Z}^d$, highlighting how the underlying structure affects the asymptotic behavior of the walk.
This paper investigates whether two independent Elephant Random Walks (ERWs) on $\mathbb{Z}$, each with a different memory parameter, can meet infinitely often, extending the work of Roy, Takei, and Tanemura. We also study the asymptotic behavior of their distance by providing an elementary and accessible proof of the classical Law of the Iterated Logarithm (LIL) for centered, continuous, self-similar Gaussian processes under a certain decay condition on the covariance kernel.