Rotational Brownian motion (astronomy) of supermassive black holes appear to be randomly aligned with respect to their host galaxies. Rotational Brownian motion (astronomy) In astronomy, rotational Brownian motion is the random walk in orientation of a binary star's orbital plane, induced by gravitational perturbations from passing stars. Consider a binary that consists of two massive objects (stars, black holes etc.) and that is embedded in a stellar system containing a large number of stars. Let formula_1 and formula_2 be the masses of the two components of the binary whose total mass is formula_3. A field star that approaches the binary with impact parameter formula_4
Fractional Brownian motion Motion are independent, increments for fractional Brownian motion are not. If H > 1/2, then there is positive autocorrelation: if there is an increasing pattern in the previous steps, then it is likely that the current step will be increasing as well. If H < 1/2, the autocorrelation is negative. The process is self-similar, since in terms of probability distributions: This property is due to the fact that the covariance function is homogeneous of order 2H and can be considered as a fractal property. FBm can also be defined as the unique mean-zero Gaussian process, null at the origin, with