Superstatistics and renewal critical events

An approach to intermittent systems based on renewal processes is reviewed. The Waiting Times (WTs)between events are the main variables of interest in intermittent systems. A crucial role is played by theclass of critical events, characterized by Non-Poisson statistics and non-exponential WT distribution. Aparticular important case is given by WT distributions with power tail. Critical events play a crucial role inthe behavior of a property known as Renewal Aging. Focusing on the role of critical events, the relationbetween superstatistics and non-homogeneous Poisson processes is discussed, and the role of RenewalAging is illustrated by comparing a Non-Poisson model with a Poisson one, both of them modulated by aperiodic forcing. It is shown that the analysis of Renewal Aging is sensitive to the presence of critical eventsand that this property can be exploited to detect Non-Poisson statistics in a time series. As a consequence,it is claimed that, apart from the characterization of superstatistical features such as the distribution of theintensive parameter or the separation of the time scales, the Renewal Aging property can give some effortto better determine the role of Non-Poisson critical events in intermittent systems.