A martingale approach for the elephant random walk
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Publication:4606138
DOI10.1088/1751-8121/aa95a6zbMath1392.60038arXiv1707.04130OpenAlexW2734373404WikidataQ105584706 ScholiaQ105584706MaRDI QIDQ4606138
Publication date: 1 March 2018
Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1707.04130
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Cites Work
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- Limit distributions for large Pólya urns
- Residual diffusivity in elephant random walk models with stops
- A survey of random processes with reinforcement
- On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications
- Functional limit theorems for multitype branching processes and generalized Pólya urns.
- Exact solution of an anisotropic 2D random walk model with strong memory correlations
- Amnestically Induced Persistence in Random Walks
- Central limit theorem and related results for the elephant random walk
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