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On elephant random walk with random memory

Author

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  • Dhillon, M.
  • Kataria, K.K.

Abstract

In this paper, we introduce the elephant random walk (ERW) with memory consisting of randomly selected steps from its history. It is a time-changed variant of the standard elephant random walk with memory consisting of its full history. At each time point, the time changing component is the composition of two uniformly distributed independent random variables with support over all the past steps. Several conditional distributional properties including the conditional mean increments and conditional displacement of ERW with random memory are obtained. Using these conditional results, we derive the recursive and explicit expressions for the mean increments and mean displacement of the walk.

Suggested Citation

  • Dhillon, M. & Kataria, K.K., 2026. "On elephant random walk with random memory," Statistics & Probability Letters, Elsevier, vol. 230(C).
    • Handle: RePEc:eee:stapro:v:230:y:2026:i:c:s016771522500255x
    DOI: 10.1016/j.spl.2025.110610
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    References listed on IDEAS

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    1. Gut, Allan & Stadtmüller, Ulrich, 2021. "The number of zeros in Elephant random walks with delays," Statistics & Probability Letters, Elsevier, vol. 174(C).
    2. Christian Gourieroux & Joann Jasiak, 2022. "Long Run Predictions," Annals of Economics and Statistics, GENES, issue 145, pages 75-90.
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