Riemann and Weierstrass walks revisited

F-Javier Almaguer, Omar González Amezcua, Javier Morales-Castillo and Roberto Soto-Villalobos

Applied Mathematics and Computation, 2018, vol. 319, issue C, 518-526

Abstract: 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.

Keywords: Discrete random processes; Random walks; Weierstrass random walk; Riemann random walk; Anomalous diffusion (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:319:y:2018:i:c:p:518-526

DOI: 10.1016/j.amc.2017.05.048

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