It has been shown by Reed that random-sampling a Wiener process at times T chosen out of an exponential distribution gives rise to power laws in the distribution.We show, both theoretically and numerically, that this power-law behaviour also follows by random-sampling Levy flights (as continuous-time random walks), having Fourier distribution with the exponent b=a.
Power Laws from Randomly-Sampled Continuous-Time Random Walks
JUG, GIANCARLO;
2007-01-01
Abstract
It has been shown by Reed that random-sampling a Wiener process at times T chosen out of an exponential distribution gives rise to power laws in the distribution.We show, both theoretically and numerically, that this power-law behaviour also follows by random-sampling Levy flights (as continuous-time random walks), having Fourier distribution with the exponent b=a.
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