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.
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