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<p>In the simple random walk, the steps are independent. In contrast, in the elephant random walk every step depends on the whole past. One extension, as suggested by Bercu et al. [<CitationRef CitationID="CR4">4</CitationRef>], is to allow for stops/delays, that is, to put mass at zero. The present paper is devoted to, what we call, the <i>Bernoulli elephant random walk</i>, which comes up naturally in that context.</p>

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Bernoulli Elephant Random Walks

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月3日

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  • Allan Gut,
  • Ulrich Stadtmüller

摘要

In the simple random walk, the steps are independent. In contrast, in the elephant random walk every step depends on the whole past. One extension, as suggested by Bercu et al. [4], is to allow for stops/delays, that is, to put mass at zero. The present paper is devoted to, what we call, the Bernoulli elephant random walk, which comes up naturally in that context.