Riemann and Weierstrass walks revisited

The Weierstrass and Riemann walks are non trivial discrete random processes to model and characterize the underlying “noise” in the dynamics of fluctuations for out of equilibrium systems, and, in more general contexts, to simulate complex dynamics like order-disorder phase transitions and anomalous diffusion properties in physical, biological and financial systems. In this work simple algorithms, implemented in GNU-R, for both Riemann and Weierstrass discrete processes are presented. Explicit formulas for the probability distributions of n steps are obtained. Finally a way to connect both random processes is commented.