TY - JOUR

T1 - Universal generation of statistical self-similarity

T2 - A randomized central limit theorem

AU - Eliazar, Iddo

AU - Klafter, Joseph

PY - 2009/8/6

Y1 - 2009/8/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=68149098760&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.103.040602

DO - 10.1103/PhysRevLett.103.040602

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C2 - 19659338

AN - SCOPUS:68149098760

SN - 0031-9007

VL - 103

JO - Physical Review Letters

JF - Physical Review Letters

IS - 4

M1 - 040602

ER -