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Reveals the characteristics of Bernoulli elephant random walks, highlighting their unique properties in random processes.
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.
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Gut et al. (2026) studied this question.
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