Continuous time random walks and south Spain seismic series

Lévy flights were introduced through the mathematical research of thealgebra or random variables with infinite moments. Mandelbrot recognizedthat the Lévy flight prescription had a deep connection toscale-invariant fractal random walk trajectories. The theory of ContinuousTime Random Walks (CTRW) can be described in terms of Lévydistribution functions and it can be used to explain some earthquakecharacteristics like the distribution of waiting times and hypocenter locationsin a seismic region. This paper checks the validity of this assumptionanalyzing three seismic series localized in South Spain. The three seismicseries (Alborán, Antequera and Loja) show qualitatively the samebehavior, although there are quantitative differences between them.