Snakes and perturbed random walks
We study some properties of random walks perturbed at extrema, which are generalizations of the walks considered, e.g., by Davis (1999) and Tth (1996). This process can also be viewed as a version of an excited random walk, recently studied by many authors. We obtain several properties related to the range of the process with infinite memory and prove the strong law, the central limit theorem, and
