Exact solutions are rare for non-Markovian random walk models even in 1D, and much more so in 2D. Here we propose a 2D genuinely non-Markovian random walk model with a very rich phase diagram, such that the motion in each dimension can belong to one of 3 categories: (i) subdiffusive, (ii)...

An important class of random walks includes those in which the random increment at time step t depends on the complete history of the process. We consider a recently proposed discrete-time non-Markovian random walk process characterized by a memory parameter p. We numerically calculate the first...

In this work we introduce a new approach to dynamical Monte Carlo methods to simulate Markovian processes. We apply this approach to formulate and study an epidemic generalized SIRS model. The results are in excellent agreement with the forth order Runge–Kutta Method in a region of...