Elephant random walks with delays

Abstract

In the simple random walk the steps are independent, viz., the walker has no memory. In contrast, in the Elephant Random walk (ERW), which was introduced by Sch\"utz and Trimper in 2004, the walker remembers the whole past, and the next step always depends on the whole path so far. One extension, as suggested in a recent paper by Bercu et al. (arXiv:1902.11220v1), is to allow for delays, that is, to put mass at zero. Our aim is to extend known result for the ordinary ERW to a Random Walk With Delays (ERWD).