Résumé : The elephant random walk (ERW) is a discrete-time random walk introduced by Schütz and Trimper (2004) in order to investigate how long-range memory affects the behavior of the random walk. Its particularity is that the next step of the walker depends on its whole past through a parameter. In this work, we investigate the validity of the central limit theorem of the ERW when the walker has only a gradually increasing memory. Our contribution ) (joint work with Mohamed El Machkouri, University of Rouen) provides a positive answer to a conjecture raised in a recent work by Gut and Stadtmüller (2022 Stat. Probab. Lett.189 109598).

Dernière modification : Thursday 27 March 2025

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