Variations of the elephant random walk

Abstract In the classical simple random walk steps are independent, that is, walker has no memory. contrast, in elephant walk, which was introduced by Schütz and Trimper [19] 2004, next step always depends on whole path so far. Our main aim is to prove analogous results when only a restricted memory, for example remembering most remote step(s), recent or both. We also extend models cover more general sizes.