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 Schütz and Trimper (2004), the next step always depends on the whole path so far. Various authors have studied further properties of the ERW. In Gut and Stadtmüller (2021b) we studied the case when the Elephant remembers only a finite part of the first or last steps. In both cases there was no separation into two different regimes as in the classical ERW. We also posed the question about what happens if she remembers a gradually increasing past. This paper will give some answers to that question. We also discuss related questions for ERW:s with delays.

在简单的随机游走中，步数是独立的，即步行者没有记忆。相比之下，在 Schütz 和 Trimper (2004) 引入的大象随机游走 (ERW) 中，下一步始终取决于到目前为止的整个路径。多位作者研究了战争遗留爆炸物的进一步特性。在 Gut 和 Stadtmüller（2021b）中，我们研究了大象只记得第一步或最后一步的有限部分的情况。在这两种情况下，都没有像经典战争遗留爆炸物那样分为两种不同的制度。我们还提出了如果她记得逐渐增加的过去会发生什么的问题。本文将对这个问题给出一些答案。我们还讨论了有关 ERW:s 延迟的相关问题。