A market choice model with random-size sampling from past customers is represented as an elephant random walk variant, with proofs of almost sure convergence of S_n/n and regime-dependent distributional limits for scaled S_n.
Rates of convergence in the central limit theorem for the elephant random walk with random step sizes.Journal of Statistical Physics, 190(10):154, 2023
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Elephant random walk with attributed steps and extractions of random sizes
A market choice model with random-size sampling from past customers is represented as an elephant random walk variant, with proofs of almost sure convergence of S_n/n and regime-dependent distributional limits for scaled S_n.