Brownian noise a white noise signal: meaning that Brownian motion is the integral of the white noise formula_2, whose power spectral density is flat: Note that here formula_4 denotes the Fourier transform, and formula_5 is a constant. An important property of this transform is that the derivative of any distribution transforms as from which we can conclude that the power spectrum of Brownian noise is Brown noise can be produced by integrating white noise. That is, whereas (digital) white noise can be produced by randomly choosing each sample independently, Brown noise can be produced by adding a random offset to each sample
Schramm–Loewner evolution evolution is a probability measure on planar curves, given as the image of Wiener measure under this map. In general the curve γ need not be simple, and the domain "D" is not the complement of γ([0,"t"]) in "D", but is instead the unbounded component of the complement. There are two versions of SLE, using two families of curves, each depending on a non-negative real parameter κ: SLE depends on a choice of Brownian motion on the boundary of the domain, and there are several variations depending on what sort of Brownian motion is used: for example it might start