Scale Invariance in Stochastic Processes
If is the average, expected power at frequency, then noise scales as
with for white noise, for pink noise, and for Brownian noise (and more generally, Brownian motion).
More precisely, scaling in stochastic systems concerns itself with the likelihood of choosing a particular configuration out of the set of all possible random configurations. This likelihood is given by the probability distribution. Examples of scale-invariant distributions are the Pareto distribution and the Zipfian distribution.
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