Fractional Brownian motion

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In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments of fBm need not be independent. fBm is a continuous-time Gaussian process B H ( t ) {\textstyle B_{H}(t)} on [ 0 , T ] {\textstyle [0,T]} , that starts at zero, has expectation zero for all t {\displaystyle t} in [ 0 , T ] {\textstyle [0,T]} , and has the following covariance function: E [ B H ( t ) , B H...

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