BERCU, Bernard; LAULIN, Lucile

doi:10.1016/j.spa.2020.11.004

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BERCU, Bernard
Institut de Mathématiques de Bordeaux [IMB]

LAULIN, Lucile
Institut de Mathématiques de Bordeaux [IMB]

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Stochastic Processes and their Applications. 2021-03, vol. 133, p. 111-128

Elsevier

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Our goal is to investigate the asymptotic behavior of the center of mass of the elephant random walk, which is a discrete-time random walk on integers with a complete memory of its whole history. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated logarithm and the quadratric strong law for the center of mass of the elephant random walk. The asymptotic normality of the center of mass, properly normalized, is also provided. Finally, we prove a strong limit theorem for the center of mass in the superdiffusive regime. All our analysis relies on asymptotic results for multi-dimensional martingales.< Leer menos

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On the center of mass of the elephant random walk

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