A unified and universal explanation for Lévy laws and 1/f noises.
Lévy laws and 1/f noises are shown to emerge uniquely and universally from a general model of systems which superimpose the transmissions of many independent stochastic signals. The signals are considered to follow, statistically, a common--yet arbitrary--generic signal pattern which may be either stationary or dissipative. Each signal is considered to have its own random transmission amplitude and frequency. We characterize the amplitude-frequency randomizations which render the system output's stationary law and power-spectrum universal--i.e., independent of the underlying generic signal pattern. The classes of universal stationary laws and power spectra are shown to coincide, respectively, with the classes of Lévy laws and 1/f noises--thus providing a unified and universal explanation for the ubiquity of these classes of "anomalous statistics" in various fields of science and engineering.
Eliazar
Iddo
I
Department of Technology Management, Holon Institute of Technology, P.O. Box 305, Holon 58102, Israel. eliazar@post.tau.ac.il
Klafter
Joseph
J
D000465:Algorithms; D008954:Models, Biological; D015233:Models, Statistical; D015398:Signal Transduction; D013269:Stochastic Processes