Limit theorems for a random walk with memory perturbed by a dynamical system
Probability
2021-02-04 v4
Abstract
We introduce a new random walk with unbounded memory obtained as a mixture of the Elephant Random Walk and the Dynamic Random Walk which we call the Dynamic Elephant Random Walk (DERW). As a consequence of this mixture the distribution of the increments of the resulting random process is time dependent. We prove a strong law of large numbers for the DERW and, in a particular case, we provide an explicit expression for its speed. Finally, we give sufficient conditions for the central limit theorem and the law of the iterated logarithm to hold.
Cite
@article{arxiv.2005.07288,
title = {Limit theorems for a random walk with memory perturbed by a dynamical system},
author = {Cristian F. Coletti and Lucas R. de Lima and Renato J. Gava and Denis A. Luiz},
journal= {arXiv preprint arXiv:2005.07288},
year = {2021}
}
Comments
We corrected a typo in the definition of the ERW