On the Elephant Random Walk with Stops Playing Hide and Seek with the Mittag–Leffler Distribution

The aim of this paper is to investigate the asymptotic behavior so-called elephant random walk with stops (ERWS). In contrast standard walk, allowed be lazy by staying on his own position. We prove that number ones ERWS, properly normalized, converges almost surely a Mittag-Leffler distribution. It allows us carry out sharp analysis ERWS. diffusive and critical regimes, we establish sure convergence also show it necessary self-normalized position ERWS in order normality. superdiffusive regime, nondegenerate variable. Moreover, fluctuation around its limiting variable still Gaussian.