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The number of zeros in Elephant random walks with delays

Allan Gut and Ulrich Stadtmüller

Statistics & Probability Letters, 2021, vol. 174, issue C

Abstract: In the simple random walk the steps are independent, whereas 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. In an earlier paper we investigated elephant random walks when the elephant has a restricted memory. Inspired by a suggestion by Bercu et al. (2019) we extended our results to the case when delays are allowed. In this paper we examine how the number of delays (that possibly stop the process) increases as time goes by.

Keywords: Elephant random walk; Delay; Number of zeros; Law of large numbers; Central limit theorem; Markov chain (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109112

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