Discrete time elephant walk noise: A noise process with full memory

Abstract

We use the Elephant Random Walk in order to model a stochastic noise process that it will incorporate complete memory in to the system. We call this process Elephant Walk Noise. We solve for the discrete time Langevin equation for a particle under the influence of a driving/drag force in the presence of complete memory. The solution of the Langevin equation showed four possible cases corresponding to different values of the friction coefficient.  These cases were then studied and analyzed.