Brownian noise Brownian noise In science, Brownian noise (), also known as Brown noise or red noise, is the kind of signal noise produced by Brownian motion, hence its alternative name of random walk noise. The term "Brown noise" does not come from the color, but after Robert Brown, the discoverer of Brownian motion. The term "red noise" comes from the "white noise"/"white light" analogy; red noise is strong in longer wavelengths, similar to the red end of the visible spectrum. The graphic representation of the sound signal mimics a Brownian pattern. Its spectral density is inversely proportional to "f" , meaning
Fractional Brownian motion Suppose we want to simulate the values of the "fBM" at times formula_12 using the Cholesky decomposition method. In order to compute formula_15, we can use for instance the Cholesky decomposition method. An alternative method uses the eigenvalues of formula_16: Note that the result is real-valued because formula_36. Note that since the eigenvectors are linearly independent, the matrix formula_39 is invertible. It is also known that where "B" is a standard Brownian motion and Where formula_47 is the Euler hypergeometric integral. Say we want to simulate an "fBm" at points formula_48. The integral may be efficiently computed by Gaussian quadrature.