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:
“I find it interesting that the meanest life, the poorest existence, is attributed to God’s will, but as human beings become more affluent, as their living standard and style begin to ascend the material scale, God descends the scale of responsibility at a commensurate speed.”
—Maya Angelou (b. 1928)
“Our bodies are shaped to bear children, and our lives are a working out of the processes of creation. All our ambitions and intelligence are beside that great elemental point.”
—Phyllis McGinley (1905–1978)