Related papers: Interevent time distribution in seismicity: a theo…
The epidemic-type aftershock sequence model (ETAS) is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power law decay ~1/t^{1+\theta} of seismicity after an earthquake) and…
In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy…
Waiting-time statistics are generated from the Olami-Feder-Christensen model and shown to mimic some aspects of real seismicity. Preliminary analysis of the model data implies a recently proposed universal scaling law for the distribution…
We develop an efficient numerical scheme to solve accurately the set of nonlinear integral equations derived previously in (Saichev and Sornette, 2007), which describes the distribution of inter-event times in the framework of a general…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
A comparative study is performed on volcanic seismicities at Icelandic volcano, Eyjafjallaj\"okull, and Mt. Etna in Sicily from the viewpoint of complex systems science, and the discovery of remarkable similarities between them is reported.…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
We consider renewal processes where events, which can for instance be the zero crossings of a stochastic process, occur at random epochs of time. The intervals of time between events, $\tau_{1},\tau_{2},...$, are independent and identically…
The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the…
The statistical properties of time intervals between significant earthquakes are found to be described by the Zipf-Mandelbrot-Tsallis-type distribution.
We introduce a generalized homogeneous function to describe the joint probability density for magnitude and duration of events in self-organized critical systems (SOC). It follows that the cumulative distributions of magnitude and of…
We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according to a given rule, and then…
In recent years, considerable attention has been paid to research and development methods able to assess the seismic energy propagation on the territory. The seismic energy propagation is strongly related to the complexity of the source and…
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
In this paper we consider random dynamical systems formed by concatenating maps acting on the unit interval $[0,1]$ in an iid fashion. Considered as a stationary Markov process, the random dynamical system possesses a unique stationary…
We perform an experimental study of the time behavior of the $\alpha$-wave events occuring in human electroencephalographic signals. We find that the fraction of the time spent in an $\alpha$-burst of time size $\tau$ exhibits a scaling…
Over the past decades much effort has been devoted towards understanding and forecasting natural hazards. However, earthquake forecasting skill is still very limited and remains a great scientific challenge. The limited earthquake…
This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments of recent experiments and observations of…
Numerical simulation of seismicity has been successfully developed and used for the two last decades. Presently, the general theory of modeling and the progress in computational techniques provide wide options for simulation of seismic and…
Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero.…