Asymptotic Properties of Generalized Elephant Random Walks (opens in new tab)

arXiv:2406.19383v2 Announce Type: replace-cross Abstract: Elephant random walk is a special type of random walk that incorporates the memory of the past to determine its future steps. The probability of this walk taking a particular step (+1 or -1) at a time point, conditioned on the entire history, depends on a linear function of the proportion of steps of that type till that time point. In this work, we consider a generalization of the elephant random walk where we investigate how the dynam...