Aging and renewal events in sporadically modulated systems

Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency

“…As an example, the first term in the r.h.s of (8), P[n(t), n(t + τ)], is the joint probability of first having a Non-Poisson event (P n ), then a Non-Poisson event after a time τ and no Poisson events in between, which becomes P[n(t), n(t + τ)] t = P n Ψ p (τ)ψ n (τ) = P n e −r p τ ψ n (τ) , (9) 5 The stationarity assumption is encoded in the coefficient P n . We have also used the fact that the Poisson process has a constant rate and, consequently, no aging [61,25,62].…”

Superstatistics and renewal critical events

“…[11,13,14,16,17], apart from the evaluation of ψ R (τ ) and Ψ S (τ ), which was done by using and approximated analytical formula [22,23]. In fact, the random shuffling, used here for the first time, is more accurate from a numerical point of view and has also the advantage of allowing to use a much larger range of the aging time with respect to the analytical formula, whose applicability is essentially limited by the maximum observed value of WTs.…”

“…Point stochastic processes and, in particular, renewal processes [15], focusing on the characterization of random time sequences, represent a natural candidate for the description of intermittent systems. As a possible model for modulated intermittent systems, the idea of superstatistics was already used in the context of renewal processes [16,17]. In this case, the slowly fluctuating intensive parameter was the rate of event production or age-specific failure rate ( ) [15,18], which will be introduced in Section 2.1.…”

“…Following this approach, the authors of Refs. [16,17] studied a NHPP with a completely random modulation of the Poisson rate, finding that the slow modulation limit, corresponding to superstatistics, leads to a situation in which the original renewal property of the unperturbed system is partially lost. This is not surprising, because the rate modulation introduces some kind of memory in the system.…”

“…[16] it was found that Renewal Aging analysis is able to detect the memory associated with the rate evolution, in the form of a non-renewal behavior of the WT statistical distributions. Renewal Aging was exploited to perform statistical analysis of artificial WT sequences [11,16,17,19] and of experimental WT sequences extracted from BQD fluorescence data [13,14] and atmospheric data [20]. The central aspect of Renewal Aging is related to the simultaneous presence of critical events and secondary events (or pseudo-events).…”