Faculté des sciences

Power laws from randomly sampled continuous-time random walks

In: Physica A: Statistical Mechanics and its Applications, 2007, vol. 375, no. 1, p. 233-238

It has been shown by Reed that random-sampling a Wiener process x(t) at times T chosen out of an exponential distribution gives rise to power laws in the distribution P(x(T))~x(T)-β. We show, both theoretically and numerically, that this power-law behaviour also follows by random-sampling Lévy flights (as continuous-time... Plus

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Summary
It has been shown by Reed that random-sampling a Wiener process x(t) at times T chosen out of an exponential distribution gives rise to power laws in the distribution P(x(T))~x(T)-β. We show, both theoretically and numerically, that this power-law behaviour also follows by random-sampling Lévy flights (as continuous-time random walks), having Fourier distribution w^(k)=e-|k|α, with the exponent β=α.