期刊
PHYSICAL REVIEW LETTERS
卷 103, 期 4, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.103.040602
关键词
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A universal mechanism for the generation of statistical self-similarity-i.e., fractality in the context of random processes-is established. We consider a generic system which superimposes independent stochastic signals, producing a system output; all signals share a common statistical signal pattern, yet each signal has its own transmission parameters-amplitude, frequency, and initiation epoch. We characterize the class of parameter randomizations yielding statistically self-similar outputs in a universal fashion-i.e., for whatever signals fed into the system. Statistically self-similar outputs with finite variance further display (i) anomalous diffusion behavior-characterized by power-law temporal variance growth-and (ii) 1/f noise behavior-characterized by power-law power spectra. The mechanism presented is a randomized central limit theorem'' for fractal statistics of random processes.
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