Many natural records exhibit long-term correlations characterized by a power-law decay of the auto-correlation function, C(s)∼s−γ, with time lag s and correlation exponent 0γ1. We study, how the presence of such correlations affects the statistics of the return intervals rq for events...

The basic assumption of common extreme value statistics is that different events in a time record are uncorrelated. In this case, the return intervals rq of events above a given threshold size q are uncorrelated and follow the Poisson distribution. In recent years there is growing evidence that...

In spite of precautions to avoid the harmful effects of extreme events, we experience recurrently, phenomena that overcome the preventive barriers. These barriers usually increase drastically right after the occurrence of such extreme events, but steadily decay in their absence. In this paper,...

The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be...

An intensity–duration–area–frequency (IDAF) function is derived for the small-scale, large-intensity limit of multifractal fields. A parameterization of the function from tropical rainfall, filmed with a digital camera in Mexico City, is being attempted. Implications of the formulae are...

Recent daily data of the Southern Oscillation Index have been analyzed. The power spectrum indicates major intrinsic geophysical short periods. We find interesting “high frequency” oscillations at 24, 27, 37, 76, 100 and 365 days. In particular the 24 days peaks may correspond to the...

We study the predictability of extreme events in records with linear and nonlinear long-range memory in the presence of additive white noise using two different approaches: (i) the precursory pattern recognition technique (PRT) that exploits solely the information about short-term precursors,...

Large changes tend to dictate the long-term dynamical behaviour of many real-world complex systems in both the natural and social sciences. We provide an analytic, microscopic analysis of extreme events arising in an adaptive population comprising competing agents (e.g. species, cells, traders,...

The Weibull distribution is often used to model the earthquake interevent times distribution (ITD). We propose a link between the earthquake ITD on single faults with the Earth’s crustal shear strength distribution by means of a phenomenological stick–slip model. For single faults or fault...

We consider nonlinear waves driven by curvature in the presence of periodically distributed obstacles. When the obstacles are small, Matano et al. (2006) proved rigorously that the propagation speed of a wave mainly depends on the opening angle of the obstacles. In this paper we first explain...