Counting statistics of

Point process model of1∕fnoise vs a sum of Lorentzians

“…The power-law distribution of the signals is observable in a large variety of systems ranging from earthquakes to the financial time series [3,12,21,30,31,32,33,34,35,37,39].…”

“…Point processes arise in different fields, such as physics, economics, cosmology, ecology, neurology, seismology, traffic flow, signaling and telecom networks, audio streams, and Internet (see, e.g., [3,11,12,13,14] and references herein). The proposed point process model [7,8,10] can been modified and useful for the modeling and analysis of self-organized systems [15], atmospheric variability [16], large flares from Gamma-ray Repeaters in astronomy [17], particles moving in viscous fluid [18], dynamical percolation [19], 1/f noise observed in cortical neurons and earthquake data [20], financial markets [21], cognitive experiments [4,22], the Parkinsonian tremors [23], and time intervals production in tapping and oscillatory motion of the hand [24].…”

Stochastic Dynamics of a Time-Delayed Ecosystem Driven by Poisson White Noise Excitation

“…However, the perturbations in the real-world environment are complicated. There are some unavoidable sparse, drastic changes in the environment, for instance sudden natural disasters, earthquakes, forest fires, floods [25][26][27]. These changes are pulse-type perturbations, which cannot be characterized by the continuous stochastic processes properly.…”