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.
Read more about this topic: Scale Invariance
Famous quotes containing the words scale and/or processes:
“Every man needs slaves like he needs clean air. To rule is to breathe, is it not? And even the most disenfranchised get to breathe. The lowest on the social scale have their spouses or their children.”
—Albert Camus (1913–1960)
“It has become a people’s war, and peoples of all sorts and races, of every degree of power and variety of fortune, are involved in its sweeping processes of change and settlement.”
—Woodrow Wilson (1856–1924)